We have the next information
m=mass=65
a=acceleration=2.70 m/s^2
We can use the next formula to find the force
\(DF=mg-ma\)where DF is the downward force and g is the gravity
\(DF=(65)(9.8)-(65)(2.7)\)\(DF=461.5\text{ N}\)A Rock is thrown Straight upward with an initial velocity of 24.5m/s where the downward acceleration due to gravity is 10.0 metre per second Square, What is the rocks displacement after 1.0 seconds
The rock was thrown upward with an initial velocity and it's displacement after one second is 19.5 m.
How does the second law of motion work?According to Newton's second law, an object's acceleration is determined by its mass and the net force that is acting on it. The body's acceleration is inversely related to its mass and directly proportional to the net force acting on it.
The displacement-time relation,
X(t) - x = vt -1/2 gt^2
X(t) = Position of object after time t
x = Initial position of object
v = Initial velocity = 24.5 m/s
g = Acceleration due to gravity = - 10.0 m/s2 (Downward)
t = time = 1 s
The displacement of rock after 1 s => X(t) - x => (24.5 x 1) - 1/2 ( 10 x 1 x 1)
=> 19.5 m
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You attach a meter stick to an oak tree, such that the top of the meter stick is 1.87 meters above the ground. Later, an acorn falls from somewhere higher up in the tree. If the acorn takes 0.311 seconds to pass the length of the meter stick, how high ℎ0
above the ground was the acorn before it fell, assuming that the acorn did not run into any branches or leaves on the way down.
The height of the acorn above the ground before falling is 2.9 m.
What is the initial velocity of the acorn?
The initial velocity of the acorn is calculated as follows;
s = ut + ¹/₂gt²
where;
u is the initial velocity of the acornt is the time of motiong is acceleration due to gravitys is the distance travelled by the acorn1.87 = 0.311u + ¹/₂(9.8)(0.311²)
1.87 = 0.311u + 0.474
0.311u = 1.396
u = ( 1.396 ) / ( 0.311 )
u = 4.489 m/s
The height the acorn falls before reaching the top velocity of 4.489 m/s is calculated as follows;
v² = u² + 2gh
where;
u is the initial velocity of the acorn = 0v is the final velocity of the acornh is the height of fall of the acornv² = 0 + 2gh
h = v² / 2g
h = ( 4.489² ) / ( 2 x 9.8 )
h = 1.03 m
The total height of the oak tree = 1.87 m + 1.03 m = 2.9 m
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t: The toy car is given a push away from the origin and released. It continues to move with a constant velocity. Sketch the force g 0' after the car is released. A cart is moving toward the right and speeding up, as shown in the diagram below. Draw arrows above the cart representing the magnitudes and directions of the net (combined) forces you think are needed on the cart at t = 0 s, t = 1 s, etc., to maintain its motion with a steadily increasing velocity. Assume that the cart is already moving at t_1. Explain the reasons for your answers. If the positive direction is toward the right, what is the sign of the force at t = 2 s in Question
The car will move at a constant speed once it is unleashed, as is assumed. Hence, there is no acceleration. Newton's second law states that a straight line along zero will appear on the graph if F=ma=m(0)=0, F=0.
Acceleration is the rate at which an object changes its velocity. It is a vector quantity, which means it has both magnitude and direction. The standard unit of acceleration is meters per second squared (m/s²).
Acceleration can be caused by forces such as gravity, friction, and electromagnetism. When a force acts on an object, it causes a change in the object's motion, resulting in acceleration.
The relationship between acceleration, velocity, and time is described by the equation a = (v_f - v_i) / t, where a is acceleration, v_f is final velocity, v_i is initial velocity, and t is time.
The effects of acceleration can be seen in everyday experiences, such as feeling pushed back into your seat when a car accelerates or feeling weightless during freefall. Understanding acceleration is important in fields such as physics, engineering, and transportation.
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Can y’all please help because my teacher didn’t really explain it to me
Answer:
8. Dinitrogen trioxide:
\({ \sf{N_{2} O_{3}}}\)
9. Nitrogen:
\({ \sf{N}}\)
10. Lithium oxide:
\({ \sf{Li_{2}O}}\)
11. Phosphorus trifluoride:
\({ \sf{PF_{3} }}\)
12. Vanadium oxide:
\({ \sf{V_{2} O_{3} }}\)
13. Silicon tetrafluoride:
\({ \sf{SiF _{4}}}\)
14. Sodium phosphide:
\({ \sf{Na_{3} P}}\)
1. A 15.0 kΩ resistor is hooked up to a 45.0 V battery in a circuit with a switch.
(a) Draw a circuit diagram for the circuit described. Label all parts and values.
(b) What is the current flowing through the resistor?
(c) What is the power dissipated by the resistor?
(a) The circuit diagram is in the image attached.
(b) The current flowing through the resistor is 0.003 A.
(c) The power dissipated by the resistor is 0.135 W.
What is current flowing through the resistor?(b) The current flowing through the resistor is calculated by applying Ohm's law as follows;
V = IR
I = V/R
where;
V is the voltageR is resistanceI = 45 V / 15,000Ω
I = 0.003 A
(c) The power dissipated by the resistor is calculated as follows;
P = IV
where;
I is the current V is the voltageP = 0.003 x 45 V
P = 0.135 W
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The superheroine Xanaxa, who has a mass of 65.1 kg , is pursuing the 78.7 kg archvillain Lexlax. She leaps from the ground to the top of a 153 m high building then dives off it and comes to rest at the bottom of a 17.5 m deep excavation where she finds Lexlax and neutralizes him. Does all this bring about a net gain or a net loss of gravitational potential energy
Answer:
There is net loss of gravitational energy .
Explanation:
When Xanaxa is on the ground , her potential energy is assumed to be zero . When she leaps to a height of 153 m , she gains gravitational energy . When she dives and reaches the surface , she loses potential energy and on reaching the ground her potential energy becomes zero . When she further goes down inside ground to a depth of 17.5 m , she loses potential energy further . Her potential energy becomes less than zero or negative .
Ultimately her potential energy changes from zero to negative in the whole process . So there is net loss of potential energy .
Melvina has a mass of 70 kg and is about to jump from the window ledge of a burning building.
The ledge is 80 m above the ground. What is Melvina's potential energy?
Melvina's potential energy is 54,880 Joules.
To calculate Melvina's potential energy, we need to use the formula for gravitational potential energy:
Potential energy = mass × gravitational acceleration × height
Potential energy is a measure of the energy an object possesses due to its position relative to other objects. In this case, Melvina's potential energy is a result of her height above the ground. As she stands on the ledge of the burning building, her potential energy is stored and can be converted into other forms of energy if she were to jump or fall. The potential energy will decrease as she descends, and it will be converted into kinetic energy (energy of motion).
Given that Melvina has a mass of 70 kg and the ledge is 80 m above the ground, we can substitute the values into the formula:
Potential energy = 70 kg × 9.8 m/s² × 80 m
Calculating this, we find:
Potential energy = 54,880 Joules
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21. Make sure carts are facing so that Velcro strips can stick together when they collide. Keep an extra 250g of mass on the cart 2 which starts at rest. Change sign on velocity center. Practice giving an initial velocity to cart 1 while cart 2 starts at rest so that after the collision both carts move as a combined object with mass m1 m2. What is the type of collision now you are practicing with two carts
Answer:
his type of shock is called inelastic
Explanation:
This exercise is for vehicle crashes, which corresponds to exercise is momentum conservation.
We must begin by defining a system formed by the two cars so that the forces during the crash have been intense and the moment is preserved.
Looking for the moments
initial. Before the crash
p₀ = m₁ v₁₀
final. After the crash
p_f = (m₁ + m₂) v
the conservation of the moment is written
p₀ = p_f
m₁ v₁₀ = (m₁ + m₂) v
This type of shock is called inelastic and has the characteristics that the kinetic energy is not conserved.
Diane is writing a summary statement of her experiment. This statement is
written.
A after data is collected and analyzed
B before writing the scientific question
C before writing the hypothesis
D at the same time data is collected.
.
A boat sails for 24 km pointed in the direction [40° S of WI. A constant current moves the boat 8 km [30° W of N]. If the trip takes 3 hours, find the boats resultant velocity
Please brainliest, really need it!!!
The resultant velocity of the boat is 7.5 km/h.
What is the resultant displacement of the boat?The resultant displacement of the boat is calculated as follows;
Sum of the vertical displacement of the boat is calculated as;
∑Fy = -24 km sin(50) + 8 km sin(60)
∑Fy = -11.5 km
Sum of the horizontal displacement of the boat is calculated as;
∑Fx = -24 km cos(50) - 8 km cos(60)
∑Fx = -19.4 km
The resultant displacement is calculated as follows;
d = √ (-11.5² + 19.4²)
d = 22.55 km
The resultant velocity of the boat is calculated as follows;
v = ( 22.55 km ) / ( 3 hrs )
v = 7.5 km/h
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If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads).
(a)
Calculate the ideal speed in (m/s) to take an 85 m radius curve banked at 15°.
(b) m/s
What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h?
Hello!
a)
For a car on an incline, we only have the normal force and force of gravity acting on the car.
The car is only experiencing a net force caused by the sine component of the force of gravity vector, which causes it to slide down the incline towards the center of the curve.
Or, as an equation:
\(F_{net} = Mgsin\phi\)
This net force produces a centripetal force. Recall the equation for centripetal force:
\(F_c = \frac{mv^2}{r}\)
In reference to the 15° angle of the incline, the cosine component of the centripetal force is equivalent to the sine component of the force due to gravity (both parallel to the incline). So:
\(F_c cos\phi = Mgsin\phi \\\\\frac{mv^2}{r}cos\phi = mgsin\phi\)
Cancel out 'm' and solve for 'v'.
\(\frac{v^2}{r}cos\phi = gsin\phi\\\\v^2 = gr \frac{sin\phi}{cos\phi}\\\\v = \sqrt{grtan\phi}\)
Plug in the given values and solve.
\(v = \sqrt{(9.8)(85)tan(15)} = \boxed{14.94 \frac{m}{s}}\)
b)
Begin by converting 20.0 km/h to m/s.
\(\frac{20 km}{hr} * \frac{1 hr}{3600 s} * \frac{1000m}{1 km} = 5.556 \frac{m}{s}\)
For this situation, we also have the force of friction present along the axis of the sine component of the force of gravity that contributes to the net force.
Recall the equation of kinetic friction:
\(F_f = \mu_k N\)
In this situation, we have the sine (vertical) component of the centripetal force as well as the cosine component of the force of gravity making up the normal force, so:
\(F_f = \mu_k (\frac{mv^2}{r}sin\phi + mgcos\phi)\)
If a curve is banked at a slower speed than appropriate, the car will tend to slide towards the center. Thus, this force of friction points up the incline, opposite to the force due to gravity. We can do another summation of forces like above.
\(\frac{mv^2}{r} cos\phi= mgsin\phi - \mu_k (\frac{mv^2}{r}sin\phi + mgcos\phi)\)
Cancel out 'm' and simplify the equation further to solve for μ.
\(\frac{v^2}{r} cos\phi= gsin\phi - \mu_k (\frac{v^2}{r}sin\phi + gcos\phi)\\\\\mu_k (\frac{v^2}{r}sin\phi + gcos\phi)= gsin\phi - \frac{v^2}{r} cos\phi\\\\\mu_k = \frac{gsin\phi - \frac{v^2}{r} cos\phi}{(\frac{v^2}{r}sin\phi + gcos\phi)}\)
Plug in values.
\(\mu_k = \frac{9.8sin(15) - \frac{5.556^2}{85} cos(15)}{\frac{5.556^2}{85}sin(15) + 9.8cos(15)} = \boxed{0.2286}\)
A student uses a motion detector to study the kinematics of a block suspended on a vertical spring that obeys Hooke’s law. The student pulls the block a distance y from equilibrium, releases it from rest, and records the speed v of the block as it passes the equilibrium position. The student repeats this process several times for different values of y. Which variables should be plotted on the horizontal and vertical axes to yield a linear graph?
When the speed of the block is plotted on the vertical axis and displacement of the block plotted on the horizontal axis, a linear graph will be obtained showing the inverse relationship between the speed of the block and the displacement of the block.
Hooke's lawHooke's law states that force or load applied to elastic material is directly proportional to the extension produced in the material. This law can be written as;
F = kx
where;
F is the applied forcek is spring constantx is extension of the materialVelocity of the blockThe speed of the block increases with decreasing displacement of the bock. This is because the kinetic energy of the block is maximum at zero displacement and minimum at maximum displacement of the block.
Thus, when the speed of the block is plotted on the vertical axis and displacement of the block plotted on the horizontal axis, a linear graph will be obtained showing the inverse relationship between the speed of the block and the displacement of the block.
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For which type of pathogens do immunizations/vaccinations help prevent?
To reduce the risk of atherosclerosis, it is important to cut down on?
The pathogen that immunization helps to prevent is virus.
To reduce the risk of atherosclerosis cut down on saturated fatty foods.
What is immunization?Immunization is defined as the prevention of pathogenic viral organisms from harming a living human host through the exposure of the host to an attenuated form of the virus to develop immunity prior to a future exposure.
Atherosclerosis is the deposition of fatty substances on the arterial wall leading to blocking of the blood vessels.
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a car accelerates from rest to a speed of 36 km/hour in 10 seconds. find
the acceleration
the distance travelled
the speed at the end of the 5th second
Answer: ok, so there should be no speed at the 5th second but there was somehow it was the car fault
∞ω∞
express the following sum with the correct number of significant figures 1.90m+134.5cm+3.62×10^5 meuo m
The sum of the figures given is determined as 362,003.245 m.
Sum of the given figures
The sum of the figures given in the question is calculated as follows;
Convert all the numbers to meter134.5 cm = 1.345 m
= 1.9 m + 1.345 m + 3.62 × 10⁵ m
= 1.9 m + 1.345 m + 362,000 m
= 362,003.245 m
Thus, the sum of the figures given is determined as 362,003.245 m.
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A ball is projected with an initial velocity 50m/s at an angle 30 degree from the top of a tower 55m high.calculate the total time the ball was on the air and the maximum horizontal distance
Time of flight = 1.6 s
Horizontal distance = 64 m
What is a projectile motion?Projectile motion is the form of motion experienced by an object or particle projected into a gravitational field, such as from the surface of the Earth, and moves along a curvilinear path only under the action of gravity.
For the given case,
h = vt + ¹/₂gt²
h = height of tower
v = initial velocity
t = time of flight
55 = 50sin30t + ¹/₂9.8t²
55 = 25t + 4.9t²
4.9t² + 25t - 55 = 0
t = 1.6 s
X = vₓt
X = horizontal distance
vₓ = horizontal velocity
t = time of flight
X = (50 x cos30) x 1.6
X = 64 m
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How would the calculation change if a typical comet in the Oort cloud is only 1 km in diameter?
When a typical comet in the Oort cloud is only 1 km in diameter, then the mass of the Oort cloud is changes to 4.18×10⁹ kg.
The mass of each comet int he Oort cloud is,
mass = density × Volume
volume of sphere = 4/3(π×r²) where, r = radius of the sphere
From the given,
diameter = 1 km
radius = Diameter / 2 = 1/2(D)
Volume of the comet = 4/3 (π×r²) = 4/3 (π× (1/2 (10)³)²)
= 4/3×(π) ×(1/8×10⁶)
Mass = density × volume, where density = 1000 kg/m³
= 1000 × 4/3×(π) ×(1/8×10⁶)
= 4.18 ×10⁹ kg
When the typical comet in the Oort cloud is only 12 km in diameter the mass of Oort cloud is 4.18×10⁹ kg.
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1) a stationary object may have______
a.potential energy b.velocity
c.kinetic energy d.acceleration
Explanation:
I think it's option a..
I think this is it!
the sun transfers heat to earth through ___ this method of heat transfer is evidence that ___ is not necessary for heat to move from place to place
Answer:
electromagnetic waves, physical contact
Explanation:
The sun transfers heat to earth through electromagnetic radiation. This method of heat transfer is evidence that direct contact is not necessary for heat to move from place to place.
What is meant by heat transfer ?Heat transfer is defined as the flow of heat or thermal energy from one point to another due to the temperature difference between the two points.
Here,
Due to the temperature difference between, heat transfer occurs between two points through various methods such as conduction, convection and radiation.
Conduction is the process of heat transfer through which heat is transferred between two objects that are in direct contact with each other. It can occur in solids, liquids and gases.
Convection is the process of heat transfer through which the heat is transferred by the movement of fluids. Air and water currents are the examples for it.
Radiation is the process of heat transfer in which the heat is transferred in the form of electromagnetic waves.
The heat energy from the sun reaches the earth through the phenomenon called electromagnetic radiation. Mainly infrared radiations carry the heat towards earth.
Unlike conduction and convection, radiation does not require any matter to transfer the heat energy.
Hence,
The sun transfers heat to earth through electromagnetic radiation. This method of heat transfer is evidence that direct contact is not necessary for heat to move from place to place.
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A population of ducks lives in an area that floods many times each year. Some of the ducks are better at finding food on dry land, while other ducks are better at finding food in wet, muddy areas. Eventually, the land around the lake permanently changes from dry soil to wet, marshy mud. How will this change to the land most likely affect the duck population? The population will remain stable because the ducks will not be affected by this kind of change. The population will eventually balance out so that there are equal numbers of both types of ducks. The population will evolve so that most ducks survive no matter how they find food. The population will evolve so that most ducks are better at finding food in wet, muddy areas.
Answer:
The answer is: The population will evolve so that most ducks are better at finding food in wet, muddy areas.Explanation:
Hope this helps! Have a great day/night!
The population of ducks will evolve so that most ducks are better at finding food in wet areas.
Natural selection:
In evolution, the individual is selected on a certain parameters by nature.
For example- Selection parameter is ability of finding food.
Here, the popution good at finding food in dry places will die and only the individuals with ability to find food in wet places will survive and reproduce.
Therefore, the population of ducks will evolve so that most ducks are better at finding food in wet areas.
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A car accelerates from 20 m/s to 30m/s in 10s
,draw velocity time graph to show cars motion.find the distance its travels by calculating the area under the graphing?
Answer:
250 m
Explanation:
Refer to the attachment for the graph. Here, we are asked to calculate the distance travelled.
⇒ Area under the graph = Distance travelled by the body
Let the distance travelled by the body be S. Area under the graph will be the area of the trapezium ABCD.Area of trapezium = ½ × Sum of parallel sides × Height
\( \twoheadrightarrow \quad \sf {S = \dfrac{1}{2}\times (AD + BC) \times OC} \\ \)
\( \twoheadrightarrow \quad \sf {S = \dfrac{1}{\cancel{2}}\times (10+30) \times \cancel{10}} \\ \)
\( \twoheadrightarrow \quad \sf {S = 1\times 50 \times 5} \\ \)
\(\twoheadrightarrow \quad \boxed{\red{\sf{ S = 250 \; m}}}\\\)
❝ Therefore, distance travelled by the body is 250 m. ❞
Three bulbs_ two of which contain different gases and one of which is empty; are connected as shown in drawing (a). Which drawing (b) - (d) best represents the system after the stopcocks are opened and the system is allowed to come to equilibrium? drawing (d) drawing (b) drawing (c}
Drawing (d) best represents the system after the stopcocks are opened and the system is allowed to come to equilibrium, as it shows equal pressure in all three bulbs.
Since the two bulbs contain different gases, the pressures in each bulb will be different. When the stopcocks are opened, the gases will flow into the empty bulb until the pressures are equalized. The final state will have equal pressure in all three bulbs.
What is an equilibrium?
An equilibrium is a state of balance or stability achieved in a chemical reaction when the forward reaction rate is equal to the reverse reaction rate. In other words, it is the point at which the concentrations of reactants and products no longer change with time, because the rates of the forward and reverse reactions are equal.
At equilibrium, the amounts of reactants and products are governed by the equilibrium constant (K), which is a measure of the relative concentrations of the reactants and products at equilibrium.
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find the current and voltage across each resistor in the given circuit.
Answer:
R1, R4: 1.3433 VR2: 0 VR3: 6.3134 VExplanation:
The resistor R2 is shorted out, so is not in the circuit. The remaining resistors are in a series circuit with a total resistance of ...
R1 +R3 +R4 = 1k +4.7k +1k = 6.7k
The current is the ratio of the applied voltage to this total resistance:
I = V/R = (9 v)/(6.7k) ≈ 1.3433 mA
The voltage across each resistor is the product of this current value and the resistance:
R1 voltage = (1 kΩ)(1.3433 mA) = 1.3433 volts
R2 voltage = 0
R3 voltage = (4.7 kΩ)(1.3433 mA) = 6.3134 volts
R4 voltage = (1 kΩ)(1.3433 mA) = 1.3433 volts
What do you do to find the manipulated variable in a line graph?
Answer: Days and Height (cm).
Explanation:
NEED HELP ASAP
what is the maximum height achieved by a track star who goes into a long jump at 12m/s at an angle of 20.0 about the horizontal? (hint 12m/s is not the horizontal component of the velocity vector.)
11.76m is the maximum height achieved by a track star who goes into a long jump at 12m/s at an angle of 20.0 about the horizontal
Define projectile motion.
An object or particle that is projected into a gravitational field, such as from the surface of the Earth, and moves along a curved route only under the influence of gravity is said to be experiencing projectile motion.
Most calculations make the assumption that the effects of air resistance are passive and insignificant in the specific instance of Earth projectile motion. Galileo demonstrated that the curved path of objects in projectile motion is a parabola; however, in the unique situation where an object is hurled directly upwards, it may also be a straight line. Such a trajectory is a ballistic trajectory, which is the study of such movements.
v = u + at
a = g = 9.8m/s2
v = 0
u = 12 sin 20
t = 12 sin 20 /9.8 = 0.42 s
s = ut +1/2 at2
s = 12sin20 + 1/2 *9.8*0.42*0.42
s = 10.9 +.864 = 11.76m
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identify each statement as an example of melting or sublimation.
Answer:
Your answers are correct
Explanation:
In my opinion, your answers are grouped in the appropriate columns.
which of the following can not happen when a light ray strikes a new medium
Answer:
amplification
Explanation:
reflection can happen
some amount of lighr get absorbed
something gets refracted
but amplification cant
Do you think Kepler will be able to detect Earth-sized planets in transit?
Answer: Less than 1% of the stars that Kepler will be looking at are closer than 600 light years. Stars farther than 3,000 light years are too faint for Kepler to observe the transits needed to detect Earth-size planets.
Explanation:
A 1.07 H inductor is connected in series with a fluorescent lamp to limit the current drawn by the lamp. If the combination is connected to a 28.9 Hz, 170 V line, and if the voltage across the lamp is to be 17.6 V, what is the current in the circuit
Answer:
0.784 A
Explanation:
From the question,
Note that the current in the circuit is the same as the current flowing through the inductor since they are both connected in series.
I = VL/XL....................... Equation 1
Where I = current flowing through the circuit, VL = Voltage drop across the inductor, XL = reactance of the inductor.
XL = 2πfL................. Equation 2
Given: f = 28.9 Hz, L = 1.07 H, π = 3.143
XL = 2(3.143)(28.9)(1.07)
XL = 194.38 Ω.
VL = V-Vf
VL = 170-17.6
VL = 152.4 V
Substitute these values into equation 1
I = 152.4/194.38
I = 0.784 A
The current in the circuit when combination is connected should be 0.784 A.
Calculation of the current:SInce
we know that
I = VL/XL....................... Equation 1
Here,
I = current flowing through the circuit,
VL = Voltage drop across the inductor,
XL = reactance of the inductor.
And,
XL = 2πfL................. Equation 2
Here
f = 28.9 Hz, L = 1.07 H, π = 3.143
So,
XL = 2(3.143)(28.9)(1.07)
XL = 194.38 Ω.
Now
VL = V-Vf
VL = 170-17.6
VL = 152.4 V
Now
I = 152.4/194.38
I = 0.784 A
hence, The current in the circuit when combination is connected should be 0.784 A.
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A baseball is popped straight up into the air and has a hang-time of 6.25 S.
Determine the height to which the ball rises before it reaches its peak. (Hint: the
time to rise to the peak is one-half the total hang-time.)
Answer:
To determine the height to which the ball rises before it reaches its peak, we need to know the initial velocity of the ball and the acceleration due to gravity. Let's assume the initial velocity of the ball is v and the acceleration due to gravity is g.
The time it takes for the ball to reach its peak is one-half the total hang-time, or 1/2 * 6.25 s = 3.125 s.
The height to which the ball rises can be calculated using the formula:
height = v * t - (1/2) * g * t^2
Substituting in the values we know, we get:
height = v * 3.125 s - (1/2) * g * (3.125 s)^2
To solve for the height, we need to know the value of v and g. Without more information, it is not possible to determine the height to which the ball rises before it reaches its peak.
Explanation:
Answer:
Approximately \(47.9\; {\rm m}\) (assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\) and that air resistance on the baseball is negligible.)
Explanation:
If the air resistance on the baseball is negligible, the baseball will reach maximum height at exactly \((1/2)\) the time it is in the air. In this example, that will be \(t = (6.25\; {\rm s}) / (2) = 3.125\; {\rm s}\).
When the baseball is at maximum height, the velocity of the baseball will be \(0\). Let \(v_{f}\) denote the velocity of the baseball after a period of \(t\). After \(t = 3.125\; {\rm s}\), the baseball would reach maximum height with a velocity of \(v_{f} = 0\; {\rm m\cdot s^{-1}}\).
Since air resistance is negligible, the acceleration on the baseball will be constantly \(a = (-g) = (-9.81\; {\rm m\cdot s^{-2}})\).
Let \(v_{i}\) denote the initial velocity of this baseball. The SUVAT equation \(v_{f} = v_{i} + a\, t\) relates these quantities. Rearrange this equation and solve for initial velocity \(v_{i}\):
\(\begin{aligned}v_{i} &= v_{f} - a\, t \\ &= (0\; {\rm m\cdot s^{-1}}) - (-9.81\; {\rm m\cdot s^{-2}})\, (3.125\; {\rm s}) \\ &\approx 30.656\; {\rm m\cdot s^{-1}}\end{aligned}\).
The displacement of an object is the change in the position. Let \(x\) denote the displacement of the baseball when its velocity changed from \(v_{i} = 0\; {\rm m\cdot s^{-1}}\) (at starting point) to \(v_{t} \approx 30.656\; {\rm m\cdot s^{-1}}\) (at max height) in \(t = 3.125\; {\rm s}\). Apply the equation \(x = (1/2)\, (v_{i} + v_{t}) \, t\) to find the displacement of this baseball:
\(\begin{aligned}x &= \frac{1}{2}\, (v_{i} + v_{t})\, t \\ &\approx \frac{1}{2}\, (0\; {\rm m\cdot s^{-1}} + 30.565\; {\rm m\cdot s^{-1}})\, (3.125\; {\rm s}) \\ &\approx 47.9\; {\rm m}\end{aligned}\).
In other words, the position of the baseball changed by approximately \(47.9\; {\rm m}\) from the starting point to the position where the baseball reached maximum height. Hence, the maximum height of this baseball would be approximately \(47.9\; {\rm m}\!\).