Answer:
The Correct Answer is
The U.S. Constitution says powers not given to the federal government belong to the states.
Explanation:
In the paragraph, Jefferson states defending the rights of states is one of the fundamental, or most significant, policies of our administration. Did that get you to remember the Tenth Amendment? It restrains the authority of the central government, defending the rights of states. It states that the central government only has the authorities listed in the Constitution. Unlisted authorities belong to the states.
Answer:
D
Explanation:
Two bodies of masses M1 and M2, when released near earth’s surface in the absence of air take time T1 and T2 to reach the ground respectively, if M1> M2, then
T1> T2
T1T1=T2
Cannot be commented
In the absence of air resistance the two bodies with masses M1 and M2 will fall at the same time. T1 = T2
What is the time of motion of the two bodies?The time of motion of the two bodies is the time taken for the two bodies to fall from the given height to ground level.
The time taken for each object to fall to ground level is determined by applying the following equation.
F = mv/t
t = mv/F
t = mv/F
where;
F is force of gravityv is the speed of the objectIn the presence of friction (air resistance), an object with big mass will take lesser time to fall to ground.
In the absence of force of friction (air resistance), every object dropped towards the earth will fall at the same time.
Thus, the two bodies with masses M1 and M2 will fall at the same time in the absence of air resistance.
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The debris from a supernova explosion is called a supernova _________.
The debris from a supernova explosion is called supernova remnants.
When a massive star reaches the end of its life, it undergoes a catastrophic explosion known as a supernova. This explosion releases an enormous amount of energy and scatters the outer layers of the star into space. The debris from a supernova explosion consists of various elements and particles, including heavy metals, dust, and gas.
These remnants are dispersed throughout the surrounding interstellar medium, enriching it with new elements and contributing to the formation of future stars and planetary systems. The debris from a supernova explosion plays a crucial role in the evolution of galaxies and the universe as a whole.
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The debris from a supernova explosion is called a supernova remnant.
When a massive star reaches the end of its life cycle and undergoes a supernova explosion, it releases an immense amount of energy and ejects a significant amount of material into space. This expelled material, consisting of gas, dust, and other particles, forms a rapidly expanding shell or cloud known as a supernova remnant.
Supernova remnants are fascinating astronomical objects that provide valuable insights into the processes involved in stellar evolution and the dispersal of heavy elements throughout the universe. They contain a mix of ionized gas, neutral gas, and dust, which emit various forms of radiation, including visible light, X-rays, and radio waves. These emissions are produced as the high-speed shock wave generated by the explosion interacts with the surrounding interstellar medium.
Over time, the supernova remnant expands and cools, gradually mixing its material with the surrounding interstellar medium. As a result, it enriches the interstellar medium with heavy elements, such as carbon, oxygen, iron, and other elements synthesized in the core of the massive star. These elements are then incorporated into subsequent generations of stars, planets, and other astronomical objects, contributing to the diversity of chemical compositions found throughout the universe.
Studying supernova remnants provides astronomers with valuable information about the life cycles of stars, the mechanisms behind supernova explosions, and the dynamics of interstellar matter. They serve as important laboratories for investigating the physical processes of particle acceleration, magnetic fields, and shock wave dynamics, contributing to our understanding of the universe's evolution.
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(b) A car driver makes an emergency stop.
The chart shows the 'thinking distance' and the 'braking distance' needed to stop the
car.
(i)
Thinking distance 9m Braking distance 14 m
Calculate the total stopping distance of the car.
Stopping distance =
(ii) The graph shows that speed affects thinking distance.
. m
(1)
Answer:9m
Explanation:
1. Siham is practicing for the marathon, she can run 1200 meters in 5 min, what is her speed in m/sec. Show all your work including the formula and units.
2. You need to get to class, 200 meters away, and you can only walk in the hallways at about 1.5 m/s. (if you run any faster, you’ll be caught for running). How much time will it take to get to your class? include formula and units.
3.Mahmoud's speed is 60 km/hr. What is the distance that he will cover in 5.5 hours. Show all your work including formula and units.
4.Mahmoud's speed is 60 km/hr. What is the distance that he will cover in 5.5 hours. Show all your work including formula and units.
1. speed = distance/time taken
= 1200/5×60
= 4 m/sec.
then Siham run 4 meters each ine second.
2. if speed = distance/time taken
then time taken= distance/ speed
= 200/1.5 = 200÷(3/2)
= 200×(2/3)
= 133.3333....sec.
then I need 133.333 sec to get to class early.
3. from the previous example
then distance = speed × time taken
= 60×5.5
= 60×(11/2)
=330 km. or 330×10³m.
then Mahmoud ❤️ covers 330km.
4.the q question is repeated.
A force of 37.0 N is required to start a 3.0 kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 37.0 N force continues, the box accelerates at 0.60 m/s^2. What is the coefficient of kinetic friction?
When a force is applied to an object resting on a surface, the frictional force acts in the opposite direction to the force applied. There are two types of frictional forces: static friction and kinetic friction.
Static friction is the force that opposes the start of motion between two surfaces, while kinetic friction is the force that opposes the motion of an object that is already moving.The coefficient of friction is a dimensionless constant that describes the relationship between the frictional force and the normal force, which is the force perpendicular to the surface. It can be used to calculate the frictional force in a given situation.
To find the coefficient of static friction, we use the formula:
fs = μsN
where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force acting on the box. Since the box is on a horizontal surface, the normal force is equal to the weight of the box, which is given by:
N = mg
where m is the mass of the box and g is the acceleration due to gravity (9.81 m/s^2). Substituting in the given values, we get:
N = (3.0 kg)(9.81 m/s^2) = 29.43 N
To find the coefficient of static friction, we need to determine the minimum force required to start the box moving. Since the force required is given as 37.0 N.
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If the rate at which the oceanic ridge is spreading is 5 cm/yr. How much farther (in kilometers) will continents A and B be from each other in one million years? Hint: Speed = Time Dis tan ce , so Distance = Speed × Time. 1 km=1000 m,1 m=100 cm. Show your work. (2)
In one million years, continents A and B will be 50 kilometers farther apart.
The rate at which the oceanic ridge is spreading is given as 5 cm/yr. To find how much farther continents A and B will be from each other in one million years, we can use the formula Distance = Speed × Time.
First, let's convert the speed from cm/yr to km/yr. Since 1 km = 1000 m and 1 m = 100 cm, we divide the speed by 100,000 to convert cm/yr to km/yr. Therefore, the speed is 5 cm/yr ÷ 100,000 = 0.00005 km/yr.
Next, we multiply the speed by the time (1 million years) to find the distance. Distance = 0.00005 km/yr × 1,000,000 years = 50 km.
Therefore, in one million years, continents A and B will be 50 kilometers farther from each other.
To summarize:
- Convert cm/yr to km/yr by dividing by 100,000.
- Multiply the speed in km/yr by the time (1 million years) to find the distance.
- The continents will be 50 kilometers farther from each other.
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An astronomer is observing a star which puzzles her. The lines in the star's spectrum indicates that the star is very hot and should therefore be blue. But the star looks reddish in photographs and in measurements of the continuous spectrum. What is one possible explanation of this puzzle
Answer:
the stars which are red in color are cool.
Explanation:
The stars which has reddish color are cool in nature while those stars which has white and blue in color are very hot in nature. The stars change its color when they becomes hotter , first the star color reddish when they are cool but with increasing temperature it changes the color from reddish to orange then yellow. After yellow it turns green and finally get blue color when the stars are very very hot.
T/F: will density be higher or lower if there are air bubbles on an object
If there are air bubbles on an object, then the density will be lower.
If there are air bubbles on an object, the density of the object will be lower. In general, density is defined as the amount of mass present in an object per unit volume of the object.
The volume of the object is fixed and the amount of mass present in it decides its density.In the case of an object containing air bubbles, the volume of the object remains the same, but the amount of mass present in it is less due to the air bubbles. This decrease in mass results in a lower density of the object.Therefore, the given statement that the density will be lower if there are air bubbles on an object is True.
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Which one of the following does Kepler's Second Law indirectly describe?
- the masses of planets - the sizes of planets - the densities of the materials that planets are made of - the speeds with which planets travel in their orbits
Kepler's Second Law indirectly describes the speeds with which planets travel in their orbits.
This law, also known as the Law of Equal Areas, states that a line connecting a planet to the sun sweeps out equal areas in equal times, implying that planets move faster when closer to the sun and slower when farther away.
According to Kepler's Second Law, a line that connects a planet to the sun, known as the radius vector, sweeps out equal areas in equal times as the planet moves along its elliptical orbit.
This means that a planet covers the same amount of area in its orbit during equal time intervals, regardless of where it is in its orbit. This implies that a planet moves faster when it is closer to the sun and slower when it is farther away.
This observation has significant implications for our understanding of planetary motion. As a planet moves closer to the sun, it experiences a stronger gravitational pull, which accelerates its motion and causes it to move faster.
Conversely, as a planet moves farther away from the sun, the gravitational pull weakens, resulting in a slower motion. This is consistent with Kepler's Second Law, which states that planets move faster in the inner parts of their orbits (when closer to the sun) and slower in the outer parts (when farther away from the sun).
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WhAT is the change IN THE entropy of 2.0kg of h2o molecules when transform at a constant pressure of 1 atm from water at 100 degrees celcius to steam at the same tEMPERATURE?
Answer:
The entropy change is 45.2 kJ/K.
Explanation:
mass of water at 100 C = 2 kg
Latent heat of vaporization, L = 2260 kJ/kg
Heat is
H = m L
H = 2 x 2260 = 4520 kJ
Entropy is given by
S = H/T = 4520/100 = 45.2 kJ/K
The entropy change during the phase change of water from liquids to steam at constant pressure and same temperatures will be zero because, Δ T is zero here.
What is entropy?Entropy is a thermodynamic parameter determining the measure of randomness in a system. Entropy of a natural reaction or change is always increasing.
According to second third law of thermodynamics the entropy change of the universe is positive always. At constant pressure the entropy change a of substance of m g is written as:
ΔS = m Cp ln T2/T1.
Where Cp is the specific heat capacity at constant pressure.
Here, the initial temperature and final temperature is same 100 degree celsius. Thus T2/T1 becomes 1 and log 1 is zero. Therefore, the entropy change in this phase change is zero.
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Why is the specific heat of water equal to unity, that is, 1.0 cal/g-°C or 1.0 kcal/kg-°C?
The specific heat of water is equal to unity due to its molecular structure and its unique properties, such as its polarity, high thermal capacity, and hydrogen bonding.
The specific heat of a substance is a measure of the amount of energy required to raise the temperature of a unit mass of that substance by one degree Celsius. The specific heat of water is an interesting topic of discussion as it has a value of 1.0 cal/g-°C or 1.0 kcal/kg-°C, which is considered as unity.
The reason the specific heat of water is equal to unity is due to its molecular structure and unique properties. Water molecules are polar in nature, meaning they have positive and negative ends. This polarity makes the water molecules bond together through hydrogen bonds.
These hydrogen bonds absorb a significant amount of energy when water is heated, which makes it difficult to raise its temperature. This property of water also allows it to absorb a significant amount of heat without a significant change in its temperature, which makes it an effective coolant in many applications.
Additionally, water has a high thermal capacity, which means it can absorb a large amount of heat without undergoing a significant temperature change. This high thermal capacity of water is due to its hydrogen bonding, which requires a lot of energy to break. As a result, water has a high specific heat, which means it requires more energy to raise its temperature compared to other substances.
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What is the mass of a gold bar that has a density of 19.3 g/mL3 and a volume of 100 cm3?
Answer:
density=mass/volume
density=19.3
mass=x
volume=100
we are looking for mass so we have to change the subject formula to m=dv
which means mass is equals to density multiplied by volume
m= 19.3 x 100
which is 1930.
What is the resistance of a light bulb if a potential difference of 120 V will produce a current of 0.5 A in the bulb?
0.0042 0
0 0.5 0
O 60 n
O 240 h
Explanation:
Remember
V = IR which is V/I = R 120 v / .5 A = 240 Ω
A ______ is like a ramp that can work while it is in _____.
A wedge is like a ramp that can work while in motion.
What is ramp?
As a tool for raising or lowering a load, an inclined plane, also referred to as a ramp, is a flat supporting surface that is tilted at an angle from the vertical direction with one end higher than the other. One of the six traditional simple machines that Renaissance scientists defined is the inclined plane.
Heavy loads are transported over vertical obstacles using inclined planes. Examples include a ramp used to load cargo into a truck, a pedestrian ascending a ramp, or an automobile or train ascending a grade.
Less force is needed to lift an object up an inclined plane than to lift it straight up, but the distance travelled is greater. Hence, a wedge is like a ramp that can work while in motion.
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physics physics physics physics
Physics is the branch of science that deals with the structure of matter and how the fundamental constituents of the universe interact. It studies objects ranging from the very small using quantum mechanics to the entire universe using general relativity.
Answer:
please ask this question separately
Explanation:
Select the four components of which the entire physical universe exists are:
energy
velocity
time
space
density
matter
The four components of the physical universe are matter, energy, space, and time.
What four components do the entire universe exists?
The four components of which the entire physical universe exists are:
Matter: All the physical substances that make up the universe, including everything from stars and planets to subatomic particles, are made of matter.
Energy: Energy is a property of matter that can be transformed, but cannot be created or destroyed. It comes in many forms, including kinetic energy, thermal energy, and electromagnetic energy.
Space: Space is the three-dimensional framework in which all matter and energy exist. It provides the canvas on which the universe unfolds and shapes the way objects interact and move.
Time: Time is the dimension in which change occurs. It is essential for the universe to exist and for events to unfold in a causal and ordered manner.
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If a pure gaseous element(hot sample of gas ) is subjected to an electrical discharge the gas will glow- it emits radiation. The resultant
If a pure gaseous element is subjected to an electrical discharge, the gas will glow because the electrical discharge causes the gas to become excited and emit radiation.
The resultant emission spectrum will be unique to the specific element, allowing scientists to identify which element is present. This phenomenon is known as spectroscopy, and it is used in various fields of science to study the composition and properties of materials. When a pure gaseous element (hot sample of gas) is subjected to an electrical discharge, the gas will glow and emit radiation. This phenomenon occurs because the electrical discharge excites the gas molecules, causing them to release energy in the form of light when they return to their lower energy states. The resultant glow and emitted radiation are characteristic of the specific element and can be analyzed using techniques like spectroscopy to identify the element's unique properties.
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I'm doing a gravity project and need a catchy title. Any ideas?
Answer:
Drop zone :)
Have a great day!!
Please rate and mark brainliest!!
Answer:
if it was a love story you could call it ¨falling for you¨ hehe though since it's a project I'm guessing it's not a love story lol.
Explanation:
To work on muscular endurance, you should use?
Answer:
Arm Workouts- with Weights.
Pushups for Upper-Body Strength.
Lunges and Squats.
Explanation: Lifting weights is one way to build muscular strength and endurance in your arms.
Pushups primarily work the pectoral muscles of the chest, starting directly below the neckline.
Brainlist please? and your welcome!
"True or False": Because action and reaction forces are equal in magnitude, they will produce the same acceleration in both objects involved.
True. Forces that are equal in magnitude always result in the same acceleration.
True. The same acceleration will result because the two objects are acting on each other.
False. Acceleration is dependent on the mass of the object that is accelerated.
False. Even though both objects experience an equal force, only one will accelerate.
True im not 100% sure but I tried.
A mass spectrometer has a velocity selector that allows ions traveling at only one speed to pass with no deflection through slits at the ends. While moving through the velocity selector, the ions pass through a 60,000-N/C E?
(a) The speed of the ions that are not deflected is -1,200,000 m/s. (b) The radius of curvature of the path of a single charged lithium ion is 2.78 x 10⁻² m. (c) The radius of curvature of the path of a singly charged fluorine ion is 3.84 x 10⁻² m.
(a) To measure the speed of the ions that are not deflected
F = q(E + v x B)
q(E + v x B) = 0
v = -E ÷ B
v = -(60,000 N/C) ÷ (0.050 T)
v = -1,200,000 m/s
(b) To determine the radius of curvature
F = (mv⁻²) ÷ r = qvB
r = (mv) ÷ (qB)
r = (1.16 x 10⁻²⁶ kg x 1,200,000 m/s) ÷ (1 x 0.050 T)
r = 2.78 x 10⁻² m
(c) To determine the radius of curvature of the path of a singly charged fluorine ion
r = (mv) ÷ (qB)
r = (1.6 x 10⁻²⁶ kg x 1,200,000 m/s) ÷ (1 x 0.050 T)
r = 3.84 x 10⁻² m
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The complete question is:
A mass spectrometer has a velocity selector that allows ions traveling at only one speed to pass with no deflection through slits at the ends. While moving through the velocity selector, the ions pass through a 60,000 N/C electric field and a 0.050 T magnetic field. The quantities v, E, and B are mutually perpendicular.
a. Determine the speed of the ions that are not deflected.
b. After leaving the velocity selector, the ions continue to move in the 0.050 T magnetic field. Determine the radius of curvature of the path of a single charged lithium ion whose mass is 1.16 x 10⁻²⁶ kg.
c. How would your answer to the above question change if instead of lithium, the ion were a singly charged fluorine ion with mass of 1.6 x 10⁻²⁶ kg?
A 750-Hz plane sound wave in seawater (13 degree C) is normally incident on a stone seawall. The sound field is found to have a maximum at the wall; the SPL there is 190 dB re 1 muPa. The SPL 0.5 m from the wall is 177 dB. (a) Use the information given about the sound field to find the impedance of the wall. (b) Find the SPL of the incident wave.
(a) The impedance of the seawall is approximately 2.13 MRayl.
(b) The SPL of the incident wave is approximately 147 dB re 1 μPa.
How to measure sound pressure levels?(a) The impedance of the seawall can be found using the measured sound pressure levels at the wall and at a distance from the wall, as follows:
First, we can use the sound pressure level (SPL) at 0.5 m from the wall to calculate the sound pressure amplitude (p0) of the incident wave:
SPL0.5m = 177 dB
p0 = 20 μPa (for a reference pressure of 1 μPa)
Next, we can use the maximum SPL at the wall to find the sound pressure amplitude at the wall (p_wall):
SPLwall = 190 dB
p_wall = 200 μPa
The impedance of the seawall (Z_wall) can then be calculated using the formula:
Z_wall = p_wall / v + vρ
where v is the speed of sound in seawater at 13°C (approximately 1532 m/s), and ρ is the density of seawater at 13°C (approximately 1025 kg/m³):
Z_wall = (200 μPa) / (1532 m/s) + (1532 m/s)(1025 kg/m³) = 2.13 MRayl (megarayls)
Therefore, the impedance of the seawall is approximately 2.13 MRayl.
(b) To find the SPL of the incident wave, we can use the formula for sound intensity (I):
I = p^2 / (2ρv)
where p is the sound pressure amplitude, ρ is the density of seawater at 13°C, and v is the speed of sound in seawater at 13°C. Solving for p:
p = sqrt(2ρvI)
We can find the sound intensity (I) using the measured SPL at 0.5 m from the wall, since the incident wave should have the same intensity everywhere in the absence of any reflections or absorption:
SPL0.5m = 177 dB
I = 10^((SPL0.5m - 120) / 10) = 2.51 x 10^-4 W/m²
Using the formula for p above:
p = sqrt(2(1025 kg/m³)(1532 m/s)(2.51 x 10^-4 W/m²)) = 0.00785 Pa
Finally, we can convert the sound pressure amplitude to an SPL using the formula:
SPL = 20 log10(p / p_ref)
where p_ref is the reference sound pressure (1 μPa):
SPL = 20 log10(0.00785 Pa / 1 μPa) = 147 dB re 1 μPa
Therefore, the SPL of the incident wave is approximately 147 dB re 1 μPa.
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How did the potential difference across the resistor change as the current flowing through the resistor changed? Did this agree with your prediction?
As the current flowing through the resistor changed, the potential difference across the resistor also changed.
According to Ohm's Law, the potential difference across a resistor is directly proportional to the current flowing through it. Therefore, if the current flowing through the resistor increases,
the potential difference across it will also increase, and vice versa. This agrees with my prediction because it is a fundamental principle of electrical circuits.
However, it is important to note that this relationship holds true only for resistors that follow Ohm's Law. For non-Ohmic resistors, the relationship between potential difference and current may not be linear, and may depend on other factors such as temperature or frequency.
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What is the current in a circuit that has a voltage of 1.5v and a resistance of 15?
Answer:
0.1 amps or A
Explanation:
I believe to calculate that you would have to use the formula V = IR and change it to:
I = V/R
I = 1.5/15
I = 0.1 amps or A
Which of the following is NOT an application of laser light?Select one:a.cutting materialb.precision surgeryc.satellite communication d.calibration of telescopes
Given:
The uses of LASER light
To find:
Which is not an application of LASER light
Explanation:
When cutting stainless steel or aluminium, LASER beams are used.
To remove warts, moles, sunspots, and tattoos in human bodies LASER lights are used.
LASER is used in communication also. Laser communication in space is the use of free-space optical communication in outer space.
One of the most important uses for lasers in astronomy is to reduce distortion on images taken with ground-based telescopes. So directly we cannot say that LASER is used for the calibration of telescopes.
Hence, calibration of telescopes is not an application of LASER light.
Which is not a way in which life is dependent on photosynthesis?
A.) Organisms breathe in the oxygen
B.) Its sugar is used as a food
C.) Helps cure disease
D.) Helps reduce global warming
Answer:
The answer is A
Explanation:
I have had this question before
hope this helps!! <3
The one that is not a way in which life is dependent on photosynthesis is that helping in cure of diseases. The correct option is C.
What is photosynthesis?Photosynthesis is a technique that plants as well as other lifeforms use to transform light energy into chemical energy that can then be released to fuel the organism's activities via cellular respiration.
Photosynthesis' primary function is to convert solar energy into chemical energy and then store that chemical energy for later use. This process powers the majority of the planet's living systems.
Photosynthesis is essential to all living things because it is the primary source of oxygen in the atmosphere.
Without photosynthetic activity, the carbon cycle would not have been possible, oxygen-requiring life would perish, and plants would perish.
Due to photosynthesis, the organisms breathe in the oxygen, sugar is used as a food, and also helps to lower down global warming.
Thus, the correct option is C.
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a 0.27-kg stone is held 1.2 m above the top edge of a water well and then dropped into it. the well has a depth of 5.2 m.
The answers to the questions are (a) 3.17J, (b) -13.75J, and (c) -16.7J, respectively.
What does it mean to have depth?The degree to which a person taking the appropriate, intellect, wisdom, insight, empathy, etc., as demonstrated by their actions or by some other mental product, such as a scholarly paper, argument, piece of art, etc. a substantial amount of such wisdom, understanding, etc. usually depths.
Briefing:Utilize U=mgy, wherein y is evaluated in relation to a standard. Here, y is calculated relative towards the well's top edge, where y is set to zero.
(a) y = 1.2m: U=mgy = (0.27kg)(9.80m/s²)(1.2m)=+3.17J
(b) y = –5.2m: U=mgy = (0.27kg)(9.80m/s²)(–5.2m) = −13.75J
(c) ΔU = Uf − Ui = (−13.75J)−(3.17J) = −16.92 = −17J
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A baseball is batted. it's a long fly ball. 5.0 seconds later the ball reaches the outfield 100 meters away and returns to the height from which it left the bat. a. what maximum height did the baseball reach?
The maximum height reached by the baseball is 24.5 meters.
To solve this problem, we can use the equations of motion for uniformly accelerated motion. The equation for the position of an object moving in a straight line with a constant acceleration is:
x = \(x_0\) + \(v_0\)t + (1/2)at²
where x is the position of the object at time t, \(x_0\) is the initial position of the object, \(v_0\) is the initial velocity of the object, and a is the acceleration of the object.
In this case, the baseball is moving vertically, so we can use the equation above to describe its motion. The initial position of the baseball is at the height from which it left the bat. The initial velocity of the baseball is the upward velocity with which it was hit. The acceleration of the baseball is the acceleration due to gravity, which is -9.8 m/s² downward.
We can use the given information to set up the following equation:
y = \(y_0\) + \(v_0\)t - (4.9)t²
where y is the height of the baseball at time t, \(y_0\) is the initial height of the baseball, \(v_0\) is the initial upward velocity of the baseball, and t is the time elapsed since the baseball was hit.
We know that the height of the baseball is 0 meters when it reaches the outfield 100 meters away (5.0 seconds later), so we can set y equal to 0 and solve for t:
0 = \(y_0\) + \(v_0\)t - (4.9)t²
(4.9)t² - \(v_0\)t - y0 = 0
This is a quadratic equation that we can solve using the quadratic formula:
t = (-\(v_0\) +/- √(\(v_0\)² - 4(4.9)(-\(y_0\)))) / (2(4.9))
We can use the given information to calculate the value of t. Since the baseball reaches the height from which it left the bat when it returns to the field, \(y_0\) is equal to the initial height of the baseball. We don't know the value of \(v_0\), but we can use the equation above to solve for it:
t = (-\(v_0\) +/- √(\(v_0\)² - 4(4.9)(-\(y_0\)))) / (2(4.9))
To solve for v0, we need to know the value of t and y0. We can use the given information to calculate t:
t = (-\(v_0\)+/- sqrt(\(v_0\)² - 4(4.9)(-\(y_0\)))) / (2(4.9))
= (-\(v_0\) +/- sqrt(\(v_0\)² + 4(4.9)\(y_0\))) / (2(4.9))
= (-\(v_0\) +/- sqrt(\(v_0\)² + 980\(y_0\))) / 9.8
= (-\(v_0\) +/- sqrt(\(v_0\)² + 980(0))) / 9.8
= (-\(v_0\) +/- sqrt(\(v_0\)²)) / 9.8
= (-\(v_0\) +/- |\(v_0\)|) / 9.8
Since t is positive, we can take the positive root:
t = (\(v_0\) + |\(v_0\)|) / 9.8
We know that t = 5.0 seconds, so we can substitute this value into the equation:
5.0 = (\(v_0\) + |\(v_0\)|) / 9.8
This equation can be rearranged to solve for v0:
\(v_0\) + |\(v_0\)| = 49
|\(v_0\)| = 49 - v0
\(v_0\)^2 = 49² - 2(49)\(v_0\) + \(v_0\)²
2(49)\(v_0\) = 49²
\(v_0\) = 49 / 2
\(v_0\) = 24.5
Now that we know the value of \(v_0\), we can substitute it into the equation for the position of the baseball to solve for \(y_0\):
y = \(y_0\) + \(v_0\)t - (4.9)t²
= \(y_0\) + 24.5t - (4.9)t²
= \(y_0\) + 24.5(5.0) - (4.9)(5.0)²
= \(y_0\) + 122.5 - 122.5
= \(y_0\)
Since \(y_0\) is equal to the initial height of the baseball, the maximum height reached by the baseball is equal to \(y_0\). Therefore, the maximum height reached by the baseball is \(y_0\) = 24.5 meters.
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An airplane moving in a straight line accelerates from 13 m/s to 21 m/s in 6.3 s. What was its acceleration assuming it is constant? Express your answer using two significant figures. Part B How far did it travel in this time? Express your answer using two significant figures.
Rounding to two significant figures, the distance traveled is approximately 107 m.
Part A:
To calculate the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 13 m/s
Final velocity (v) = 21 m/s
Time (t) = 6.3 s
Substituting the values into the formula:
acceleration = (21 m/s - 13 m/s) / 6.3 s
acceleration = 8 m/s / 6.3 s
Rounding to two significant figures, the acceleration is approximately 1.3 m/s².
Part B:
To calculate the distance traveled, we can use the formula:
distance = (initial velocity + final velocity) / 2 * time
Substituting the values into the formula:
distance = (13 m/s + 21 m/s) / 2 * 6.3 s
distance = 34 m/s / 2 * 6.3 s
Rounding to two significant figures, the distance traveled is approximately 107 m.
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The airplane's acceleration assuming it is constant is approximately 1.27 m/s^2, and it traveled approximately 107.94 meters in 6.3 seconds.
The acceleration of the airplane can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 13 m/s
Final velocity (v) = 21 m/s
Time (t) = 6.3 s
Using the formula, we can substitute the given values:
acceleration = (21 m/s - 13 m/s) / 6.3 s
Simplifying the equation, we have:
acceleration = 8 m/s / 6.3 s
Calculating this, we get an acceleration of approximately 1.27 m/s^2 (rounded to two significant figures).
Now, to find the distance traveled by the airplane, we can use the equation:
distance = (initial velocity + final velocity) / 2 * time
Substituting the given values:
distance = (13 m/s + 21 m/s) / 2 * 6.3 s
Simplifying the equation, we have:
distance = 34 m/s / 2 * 6.3 s
Calculating this, we get a distance of approximately 107.94 meters (rounded to two significant figures).
Therefore, the airplane's acceleration assuming it is constant is approximately 1.27 m/s^2, and it traveled approximately 107.94 meters in 6.3 seconds.
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Two hockey pucks with mass 0.1 kg slide across the ice and collide. Before
the collision, puck 1 is going 15 m/s to the east and puck 2 is going 12 m/s to
the west. After the collision, puck 2 is going 15 m/s to the east. What is the
velocity of puck 1?
A. 12 m/s west
B. 15 m/s east
C. 15 m/s west
D. 12 m/s east
The velocity of pluck 1 is 12 m/s west.
What is the conservation of momentum?The principle of the conservation of the linear momentum states that momentum before collision is equal to momentum after collision.
Now given that;
m1u1 + m2u2 = m1v1 + m2v2
(0.1 * 15) - (0.1 * 12) = 0.1* v + (0.1 * 15)
1.5 - 1.2 = 0.1v + 1.5
0.3 - 1.5 = 0.1v
v = -1.2/0.1
v = - 12 m/s
Hence, the velocity of pluck 1 is 12 m/s west.
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