A certain sea cow can paddle 2.0 m/s in still water. If she attempts to cross a river, from the south bank to the north with a current of 3.0 m/s flowing toward the east by paddling entirely perpendicularly to the flow of the river, in what direction will she be traveling relative to an observer on shore
Answers
Answer:
v = 3.6m / s , θ = 56º
Explanation:
This is a relative speed exercise, let's use the Pythagorean theorem
v = √ (v₁² + v₂²)
where v₁ is the speed of the sea still water and v₂ the speed of the current
let's calculate
v = √ (2² + 3²)
v = 3.6m / s
to find the direction we use trigonometry
tan θ = v₂ / v₁
θ = tan⁻¹ (v₂ / v₁)
let's calculate
θ = tan⁻¹ (3/2)
θ = 56º
Related Questions
The length of a simple pendulum is 0.80 m and the mass of the "bob" at the end is 0.31 kg. The pendulum is pulled away from equilibrium at an angle of 6.8 degrees and released from rest.
a. What is the angular frequency of the motion?
b. Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth.
c. What is the bob's speed as it passes through the lowest point of the swing?
Answers
a) angular frequency of the motion is ω = 3.5s⁻¹
b) total mechanical energy of the bob is T.M.E = 0.029J
c) bob's speed at the lowest point is V= 0.43m/s.
A mechanical device that oscillates or sways is known as a simple pendulum. The gravitational force is primarily responsible for this motion, which takes place in a vertical plane.
Given,
Length of a simple pendulum, L = 0.80m
Mass of the bob, m = 0.31 kg
h= L- LcosΘ = L (1 - cosΘ)
a) Angular frequency, ω = 2π / T
where, T = 2π √(L/g)
ω = 2π / 2π √(g/L)
ω =√(9.8 / 0.80) s⁻¹
ω = 3.5s⁻¹
b) Total mechanical energy, T.M.E = (K.E.)ₐ + (P.E.)ₐ
As (K.E.)ₐ = 0
(P.E.)ₐ =mgh
T.M.E = 0 + mgh, where h = L (1-cosΘ)
T.M.E = ngL (1-cosΘ)
= 0.31*9.8*0.80(1-0.988)
= 0.029J
Thus, T.M.E = 0.029J
c) bob's speed at the lowest position, V
TMEb = 0.029J
(KE)b + (PE)b = 0.029J
1/2mV² + 0 = 0.029J
V =√(2*0.029/m)
V = 0.43m/s
So, the speed at the lowest point is V= 0.43m/s.
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17. A ball falling from a building has a kinetic energy of 2000 J and potential
energy of 2376 J. What is the mechanical energy of the ball?
Imc
Answers
Answer:
C. 4736J
Explanation:
The mechanical energy of ball is the sum of its kinetic energy and potential energy at any point;
Mechanical energy = kinetic energy + potential energy
Given:
kinetic energy = 2000J
potential energy = 2376J
So;
Mechanical energy = 2000J + 2376J = 4736J
A person pulls a box across the floor with a rope. The rope makes an angle of 40 degrees tot he horizontal, and a total of 125 newtons of force is applied. How much work is done if the box is pulled for 25 meters?
Answers
Answer:
The angle formed of the rope with the surface = 40°
Force applied = 125Newtons
The displacement covered by the box =25metres
W= FDcos theta
[125×40×cos(40°) ] Joules
= [ (3125×0.76604444311)]Joules
= 2393.88888472 joules(ans)
Hope it helps
Why must humans limit their exposure to X-rays and gamma rays?
A. The rays can change molecules and atoms in the body into ions.
B. Exposure can cause the human body to give off heat.
O C. Even a small amount of radiation can burn the skin.
D. These rays act similarly to microwaves on the human body.
Answers
Answer:
A. The rays can change molecules and atoms in the body into ions.
16 of 20:
Select the best answer for the question.
16. What happens to a substance at critical temperatures?
O A. The substance changes its state if it continues gaining or losing thermal energy.
O B. The substance can't lose any more thermal energy.
O C. The substance can't change its state, only its temperature.
O D. The substance changes its state only if it gains thermal energy.
Answers
At the critical temperatures of the substance, the substance can't lose any more thermal energy. Hence, option B is correct.
At the critical temperature, the properties of the liquid and gas phases become difficult to differentiate, and the substance exhibits particular type of behavior such as infinite compressibility and a lack of surface tension.
Additionally, at the critical temperature, the substance reaches its maximum vapor pressure, and any further increase in temperature and pressure will not cause it to change its state but only its density and hence, it cannot lose any more thermal energy from itself.
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Callisto is a moon of Jupiter
(mass= 1.90 x 1027 kg), which orbits
the planet with a period of 16.9 days.
What is the radius of its orbit?
[?] x 10¹ m
Coefficient (green)
Exponent (yellow)
Enter
Answers
8.27 x 1013 meres is the orbital radius.
Additional details:-Jupiter's mass, 1.9 x 1027 kg, and the time interval, 16.9 days, are equal to 1.46 x 106 seconds. The radius is needed, thus r. Solution
The moon must be held in its orbit by a gravitational force equal to the centripetal force between Jupiter and the moon.
6.67 x 10⁻¹¹ N/m²kg
2 x 1.9 x 10/27 x 1.46 x 10'6 / 4 r = 6.85 x 102'7 G = 6.67 x 10'11 N/m2kg2 r = 8.27 x 10'7
What distinguishes Callisto, a huge moon orbiting Jupiter, from all other large moons in the solar system?The second-largest moon in Jupiter's orbit and the third-largest moon in the solar system is called Callisto. Of all the objects in our solar system, its surface has the most craters.
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17 1. Which statement about Kepler's law of harmonies is correct?
A. There is a direct relationship between the orbital period and the radius of orbit.
B. There is an indirect relationship between the orbital period and the radius of orbit.
C. The smaller a planet's orbital period, the greater is its radius of orbit.
D. The smaller a planet's radius of orbit, the greater is its orbital period
Answers
Answer:
B
Explanation:
Let T be the orbit period and a be the radius of orbit.
For T^2= k× a^3 (k is a constant)
there seems to be an indirect relationship between two variables.
The figure shows a jet engine suspended beneath the wing of an airplane. The weight of the engine is 14900 N and acts as shown in the figure. In flight the engine produces a thrust of 61500 N that is parallel to the ground. The rotational axis in the figure is perpendicular to the plane of the paper. With respect to this axis, find the magnitude of the torque due to (a) the weight and (b) the thrust.
Answers
We have that for the Question, it can be said that With respect to this axis, the magnitude of the torque due to the weight and ,the thrust is
TW=19740N-mTT=130387.39N-mFrom the question we are told
The figure shows a jet engine suspended beneath the wing of an airplane. The weight of the engine is 14900 N and acts as shown in the figure. In flight the engine produces a thrust of 61500 N that is parallel to the ground. The rotational axis in the figure is perpendicular to the plane of the paper. With respect to this axis, find the magnitude of the torque due to (a) the weight and (b) the thrust.
a)
Generally the equation for the Torque due to weight is mathematically given as
\(TW=Engine weight*2.50*sin32\\\\TW=14900*2.50*sin32\)
TW=19740N-m
b)
Generally the equation for the Torque due to thrust is mathematically given as
\(TT=Engine thrust*2.50*cos32\\\\TT=61500*2.50*cos32\\\\\)
TT=130387.39N-m
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What's the kinetic energy of an object that has a mass of 30 kilograms and moves with a velocity of 20 m/s?
Question 16 options:
A)
12,000 J
B)
2,940 J
C)
6,000 J
D)
5,880 J
Answers
the kinetic energy of an object that has a mass of 30 kilograms and moves with a velocity of 20 m/s is 6,000 J. Option C is correct answer.
The kinetic energy of an object that has a mass of 30 kilograms and moves with a velocity of 20 m/s can be calculated by using the formula:
K.E = 1/2 mv²
Where, K.E = Kinetic energy of the objectm = Mass of the objectv = Velocity of the object
Putting the given values in the above formula:
K.E = 1/2 mv²K.E = 1/2 × 30 kg × (20 m/s)²K.E = 1/2 × 30 × 400K.E = 6000 joules
The correct answer is C.
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Conducting an experiment without a theory, assumptions, or expectations can lead to what issue?
Answers
Answer:
When accounting for threats to validity in their study design, researchers must make assumptions about their environment. If any of these assumptions prove to be false, then it is more difficult to properly interpret the results of the experiment.
Explanation:
how to find half life
Answers
Answer: The half-life of a reaction is the time required for the reactant concentration to decrease to one-half its initial value. The half-life of a first-order reaction is a constant that is related to the rate constant for the reaction: t1/2 = 0.693/k.
Explanation:
two particles with equal charge experiences a force of 12 nN where they are 30 cm apart. what is the magnitude of the charge on each particle
Answers
Considering the Coulomb's Law, the magnitude of the charge on each particle is 4.2426 C.
Definition of Coulomb's LawCoulomb's law or law of electrostatics is the relationship between the interactions of electric charges, that is, it explains the force experienced by two electric charges at rest.
This law says that the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them, expressed mathematically as:
\(F=k\frac{Qq}{d^{2} }\)
where:
F is the electrical force of attraction or repulsion. It is measured in Newtons (N).Q and q are the values of the two point charges. They are measured in Coulombs (C).d is the value of the distance that separates them. It is measured in meters (m).k is a constant of proportionality called the Coulomb's law constant. It depends on the medium in which the charges are located. Specifically for vacuum k is approximately 9×10⁹ \(\frac{Nm^{2} }{C^{2} }\).The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign.
Magnitude of the charge on each particleIn this case, you know that:
F= 12 nN= 1.8×10⁻⁸ N (being 1 nN= 1×10⁻⁹ N)k= 9×10⁹ \(\frac{Nm^{2} }{C^{2} }\)Q= qd= 30 cm= 0.3 m (being 100 cm= 1 m)Replacing in the Coulomb's Law:
\(1.8x10^{-8} N=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{Qq}{(0.3 m)^{2} }\)
Being Q=q:
\(1.8x10^{-8} N=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{q^{2} }{(0.3 m)^{2} }\)
Solving:
1.8×10⁻⁸ N÷ 9×10⁹ \(\frac{Nm^{2} }{C^{2} }\)= q²÷ (0.3 m)²
2×10⁻¹⁸ C²/m²= q²÷ (0.3 m)²
2×10⁻¹⁸ C²/m²= q²÷ 0.09 m²
2×10⁻¹⁸ C²/m² ×0.09 m²= q²
1.8×10⁻¹⁹ C²= q²
√1.8×10⁻¹⁹ C²= q
4.2426 C= q= Q
Finally, each charge has a value of 4.2426 C.
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Which instrument would make rice vibrate easier, a tuba or a flute? Explain why. Hint: think about the difference between high and low notes in terms of vibrating atoms.
Answers
Answer:
I assume the higher notes would make the rice vibrate more easily, so a flute.
how many times larger than a centigram is a dekagram
Answers
Answer:
A dekagram is thousand (1000) times larger than a centigram.
Explanation:
→ [1 dekagram = 1,000 centigrams]
→ 1 dekagram = 10 grams
→ 10 grams = 100 decigrams
→ 100 decigrams = 1,000 centigrams
mechanical advantage describes how simple machines can___________
a. increase the amount of work being done.
b. change the total amount of work that is done
c. allow you to use less force to do the same amount of work
d. allow you to use more force to do the same amount of work
Answers
Answer:
The correct answer is c) allow you to use less force to do the same amount of work.
Ilus
A bat bounces a sound wave off a
bird 19.4 m away, and hears the
echo after 0.117 s. What is the
speed of sound in the air?
(Hint: It is not necessarily 343 m/s.)
(Unit = m/s)
Answers
Answer:
332m/s
Explanation:
We know the formula for velocity is v=d/t, but this particular question is asking about an echo. The problem tells us the distance to the bird from the bat, which is 19.4. To find the echo, you need to find the distance from the bat to the bird and back.
So
19.4 x 2 = 38.8
And then plug into the equation
v = 38.8 / 0.117
= 332m/s
Hooke’s Law Problem:
A ball of mass m = 2.60 kg, starting from rest, falls a vertical distance h = 55 cm before striking a vertically coiled spring, which compresses an amount BY = 15 cm. Determine the spring stiffness constant of the spring. Assume the spring has negligible mass, and ignore air resistance. Measure all distances
from the point where the ball first touches the uncompressed
spring (y=0 at this point).
Answers
The spring stiffness constant of the spring is 1276.44 N/m.
We know that Hooke’s Law is given by, F = -kx, where F is the force applied to an object, x is the displacement caused by the force, and k is the spring constant.
Therefore, the spring stiffness constant of the spring is given by k = -F / x.Let us first determine the potential energy of the ball, which will be equal to the kinetic energy of the ball when it strikes the spring. We can use the formula, PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the vertical distance fallen by the ball.
Therefore, the potential energy of the ball is given by,PE = mgh= 2.60 kg × 9.81 m/s² × 0.55 m= 14.38 JNow, the ball will transfer all its potential energy to the spring, which will store it as potential energy in the form of elastic potential energy. Therefore, the elastic potential energy stored in the spring is given by, PE = (1/2)kx², where x is the compression of the spring.
Therefore, we have,PE = (1/2)kx²
= (1/2)k (0.15 m)²
= 0.01125 k J
Setting the two expressions for PE equal to each other, we get,1
4.38 J = 0.01125 k JK
= (14.38 J) / (0.01125 J/k)
= 1276.44 N/m
Therefore, the spring stiffness constant of the spring is 1276.44 N/m.
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Two ropes are attached to a tree, and forces of F⃗ 1=2.0iˆ+4.0jˆN and F⃗ 2=3.0iˆ+6.0jˆN are applied. The forces are coplanar (in the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.
Answers
Answer:
We can see that the 2 forces are being applied in the same direction
So the resultant force will be larger than the given forces
Resultant force = (2i + 4j) + (3i + 6j)
R = 5i + 10j
Magnitude of the resultant force :
R² = i² + j²
R² = 25 + 100
R = \(\sqrt{125}\) = \(5\sqrt{5}\)
Direction of the resultant force:
Tan Θ = Vertical component of force / Horizontal component of force
Tan Θ = 10 / 5
Tan Θ = 2
Θ = Arctan (2)
Θ = 63.4 degrees
Direction is 63.4 degrees in the NE direction
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A) The resultant ( net force ) = 5i + 10 j
B) The magnitude and direction of this net force
magnitude of net force = 5√5 direction of net force = 63.4° NEGiven that :
The vector forces are coplanar ( In the same plane and direction )
A) resultant force = (2i + 4j) + (3i + 6j) = ( 2 + 3 ) i + ( 4 + 6 ) j
= ( 5 i + 10 j )
B ) Calculate The magnitude and direction of the net force
i) Magnitude of the force
R² = ( i² + j² )
= ( 5² + 10² )
= 25 + 100
∴ R = √ (25 + 100) = 5√5
ii) Determine the direction of resultant force
Tan ∅ = opposite / adjacent ( vertical force ( j ) / horizontal force ( i ) )
= 10 / 5 = 2
∅ = arctan ( 2 ) ≈ 63.4°
∴ direction of resultant force = 163.4° NE
Hence we can conclude that the resultant ( net force ) = 5i + 10 j and The magnitude and direction of this net force
magnitude of net force = 15 direction of net force = 1.107° NELearn more : https://brainly.com/question/24034108
A long straight wire carrying a current of 3A flowing in a direction parallel to the unit vector 1 (i+j+ k) is placed in a √√3 --↑ this is the a magnetic field of (0.75i + 0.4k)T. What is the magnetic force per unit length of the wire? A. (0.69i-0.61j - 1.3k )N/m.. B. (0.39i-0.4j-2.3 k )N/m C.(0.49i-0.51j - 1.37k )N/m D. (0.59-0.71j-0.13k )N/m
Answers
The magnetic force per unit length of the wire is (C) (0.49i - 0.51j - 1.37k) N/m.
To calculate the magnetic force per unit length of the wire, we can use the formula:
F = I * (L x B),
where F is the force, I is the current, L is the length vector of the wire, and B is the magnetic field.
Given:
Current, I = 3A
Length vector, L = √√3 * (i + j + k)
Magnetic field, B = 0.75i + 0.4k
Let's calculate the cross product of L and B:
L x B = | i j k |
|√√3 √√3 √√3|
|0.75 0 0.4|
To evaluate this cross product, we calculate the determinants:
(i) component: (√√3 * 0 - √√3 * 0.4) = -0.4√√3
(j) component: (-√√3 * 0.75 - √√3 * 0) = -0.75√√3
(k) component: (√√3 * 0.75 - √√3 * 0) = 0.75√√3
Now, multiply the cross product by the current:
F = 3A * (-0.4√√3i - 0.75√√3j + 0.75√√3k)
Simplifying this expression gives:
F = (-1.2√√3i - 2.25√√3j + 2.25√√3k) N
Therefore, the magnetic force per unit length of the wire is approximately (-1.2√√3i - 2.25√√3j + 2.25√√3k) N/m.
Comparing the given answer options, the closest match is C. (0.49i - 0.51j - 1.37k) N/m.
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Water vapor is less dense than ice because:
a. molecules in the gas phase are in constant motion.
b. molecules in the gas phase have more potential energy than in solids.
c. molecules in the gas phase have more kinetic energy than in solids.
d. gaseous molecules have less mass.
e. molecules in the gas phase have more space between them than in solids,
Answers
Answer:
The correct answer is option E
Explanation:
Relative density of the different phases of the same compound like water are basically determined by their number of molecules per volume when each of the molecules have the same mass in each of their phases.
Now, for the water vapor phase, it's molecules have very little interaction with themselves and so they are at large distance apart, whereas in ice(solid), molecules are in continuous contact with each other because they are at close distance between each other. Therefore, it's obvious that there are less molecules per liter in water vapour than in ice, and thus the density is smaller.
The correct answer is option E
I want you to think about each of these scenarios, what do you think will happen after? I just want you to think about it, and write a little about what is going to happen.
2. A truck is moving at 20 mph. Your car is standing still at a light and the truck crashes into you before the driver has a chance to step on the brakes.
3. You are driving your car at 20 mph. A bicycle right ahead of you suddenly stops and you crash into it before you have a chance to step on the brakes.
4. A bicycle is moving at 20 mph. Your car is stopped for a light and the bicycle crashes into you.
Answers
26) Star A and star B are the same surface temperature. Star A has twice the radius as star B. How does the amount of energy radiated per unit area from the surface of A compare to surface of B?
Answers
Answer:
1/4
Explanation:
Total radiation energy depends on temperature, so \(E_A=E_B\)
Radius \(R_A=2R_B\)
so the surface area \(S_A=4 S_B\)
energy per unit area
\(\frac{E_A}{S_A}=\frac{1}{4}\frac{E_B}{S_B}\)
What is the period of revolution of a satellite with mass (m) that orbits the earth in a circular path of radius 7480 km (about 1100 km) above the surface of the earth)?
Answers
When a mass (m) that orbits the earth in a circular path of radius 7480 km (about 1100 km) above the surface of the earth), the period of revolution of the given satellite is approximately 8207 seconds or 2.28 hours.
The period of revolution of a satellite with mass (m) that orbits the earth in a circular path of radius 7480 km (about 1100 km) above the surface of the earth) can be determined by using Kepler's third law which relates the period of revolution of a satellite to the average radius of its orbit.
Kepler's third law states that the square of the period of revolution of a satellite is proportional to the cube of the average radius of its orbit.
Mathematically, the law can be expressed as: T² = (4π² / GM) × R³Where T is the period of revolution, G is the gravitational constant, M is the mass of the earth, and R is the average radius of the orbit of the satellite.
To find the period of revolution of the given satellite, we can substitute the given values in the equation: R = 7480 km + 6370 km = 13850 kmM = 5.97 × 10²⁴ kgG = 6.67 × 10⁻¹¹ Nm²/kg²T² = (4π² / GM) × R³T² = (4π² / (6.67 × 10⁻¹¹ × 5.97 × 10²⁴)) × (13850 × 10³)³T² = 6.7182 × 10¹⁴ seconds²
Taking the square root of both sides, we get:T = 8.2079 × 10³ seconds
Therefore, the period of revolution of the given satellite is approximately 8207 seconds or 2.28 hours.
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A boy slides a book across the floor, using a force of 5 N over a distance of 2
m. What is the kinetic energy of the book after he slides it? Assume there is
no friction.
A. 5 J
B. 10 J
C. 20 J
D. 2.5 J
SUBMIT
Answers
The kinetic energy of the book after it is slids a distance of 2 meters will be 10 Joules.
How to determine the kinetic energy of an object?The work-energy theorem states that "the work done on an object is the change in its kinetic energy".
Hence;
Kinetic energy = work done
Note that: work-done is expressed as:
Work done = f × d
Where f is force applied and d is distance traveled.
Given that:
Force applied f = 5 newton
Distance d = 2 meters
Work done = ?
Plug these values into the above formula and solve for the workdone.
Work done = f × d
Work done = 5N × 2m
Work done = 10Nm
Work done = 10 Joules
Therefore, the kinetic energy is 10 Joules.
Option B) 10 J is the correct answer.
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Drag each label to the correct location on the chart.
Sort the items based on whether they are simple machines or compound machines.
Answers
Answer:
whatttttttttttttttttttttttttttt are the items we have to classify into simple machines and compound machine
when a torque is acting on a fly wheel the angular velocity of the fly wheel changes from 10rad/sec to 25rad/sec in 5sec.what will be the magnitudes of the angular acceleration of the fly wheel?
Answers
Hello!
We can use the following angular kinematic equation to solve:
α = Δω/Δt, or (ωf-ωi)/t
Plug in the given values:
α = (25 - 10)/5 = 15/5 = 3 rad/sec²
HELP CHECK ANSWERS ONLY 3 QUESTIONS:
1. If you took your weight first at sea level and then on top of a very tall mountain, you would find that your weight:
a. decreases
b. stays the same **
c. increases
2. Smaller masses experience more gravitational force than bigger masses.
A. True
B. False **
3. An asteroid moves away from our planet. What happens to the gravitational attraction between it and the earth as it zooms away?
a. It decreases. **
b. It increases.
c. It does not change.
d. It becomes zero.
Answers
Answer:
answer 1 is A, Answer 2 is A, Answer 3 is c
When an asteroid moves away from our planet the gravitational attraction between it and the earth as it zooms away increases.
What is gravitational force?The term gravitational force is a force that is attractive and acts between any two masses on the earth surface.
If you took your weight first at sea level and then on top of a very tall mountain, you would find that your weight increases.
It is false that Smaller masses experience more gravitational force than bigger masses.
When an asteroid moves away from our planet the gravitational attraction between it and the earth as it zooms away increases.
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what is the entropy of a system where W=3? use the statistical definition of entropy.
Answers
The change in entropy of the system is 819 JK.
Entropy, which is sometimes assumed to represent a measure of "disorder" (the higher the entropy, the worse the disorder), is a measurement of the number of possible arrangements of a system in statistical mechanics.
The amount of heat transferred, Q = 3 J
Temperature of the system, T = 273 K
The change in entropy,
ΔS = QT
ΔS = 3 x 273
ΔS = 819 JK
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An object traveling at 1.5 rad
accelerates at 0.75d for 12
S
seconds. What is the object's final
velocity?
Answers
The object's final velocity, given the data is 10.5 rad/s
What is acceleration?This is defined as the rate of change of velocity which time. It is expressed as
a = (v – u) / t
Where
a is the acceleration v is the final velocity u is the initial velocity t is the time How to determine the final velocityThe following data were obtained from the question
Initial velocity (u) = 1.5 rad/sAcceleration (a) = 0.75 rad/s²Time (t) = 12 sFinal velocity (v) = ?The final velocity can be obtained as follow:
a = (v – u) / t
0.75 = (v – 1.5) / 12
Cross multiply
v – 1.5 = 0.75 × 12
v – 1.5 = 9
Collect like terms
v = 9 + 1.5
v = 10.5 rad/s
Thus, the final velocity of the object is 10.5 rad/s
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What happens to solar radiation when it is absorbed
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Answer:
Absorbed sunlight is balanced by heat radiated from Earth's surface and atmosphere. ... The atmosphere radiates heat equivalent to 59 percent of incoming sunlight; the surface radiates only 12 percent. In other words, most solar heating happens at the surface, while most radiative cooling happens in the atmosphere