Question 1

A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outwards with a speed of 20 m/s.It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10 m/s²

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Question 2

An object is shot from the back of a railroad flatcar moving at 40 km/h on a straight horizontal road.The launcher is aimed upward, perpendicular to the bed of the flatcar.The object falls:

Accepted Answer

The object maintains the horizontal velocity of the flatcar due to inertia, so when it is shot upward and falls back down, it does so in a path that keeps it above the flatcar, assuming no external horizontal forces act on it.

Question 3

A large cannon is fired from ground level over level ground at an angle of 30° above the horizontal.The muzzle speed is 980 m/s.Neglecting air resistance, the projectile will travel what horizontal distance before striking the ground?

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Question 4

A particle moves at constant speed in a circular path.The instantaneous velocity and instantaneous acceleration vectors are:

Accepted Answer

The instantaneous velocity vector of a particle moving in a circular path is always tangent to the circle at the particle's position, while the instantaneous acceleration vector (centripetal acceleration) is always directed towards the center of the circle, making them perpendicular to each other.

Question 5

A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s.Using g = 10 m/s², the distance from launching to landing points is:

Accepted Answer

The time of flight can be calculated using the vertical component of the initial velocity and the acceleration due to gravity. The time to reach the maximum height is $t = \frac{v_{vertical}}{g} = \frac{20 m/s}{10 m/s^2} = 2 s$. Since the motion to the maximum height and back down is symmetrical, the total time of flight is $2t = 4 s$. The horizontal distance covered in this time, using the horizontal component of the velocity, is $distance = v_{horizontal} \times time = 30 m/s \times 4 s = 120 m$.

Question 6

A bomber flying in level flight with constant velocity drops a bomb before it is over the target.Neglecting air resistance, which one of the following is NOT true?

Accepted Answer

The horizontal velocity of the plane remains constant, so it does not equal the vertical velocity of the bomb at the moment it hits the target. The vertical velocity of the bomb is only affected by gravity, causing it to accelerate downwards towards the target.

Question 7

An airplane makes a gradual 90°turn while flying at a constant speed of 200 m/s.The process takes 20.0 seconds to complete.For this turn the magnitude of the average acceleration of the plane is:

Accepted Answer

We can use the formula for centripetal acceleration:

a = v^2/r

where v is the constant speed of the plane and r is the radius of the turn.

To find the radius, we can use the formula for the length of an arc:

s = rθ

where s is the length of the arc (in this case, the distance traveled during the turn), θ is the angle of the turn (90 degrees in this case), and r is the radius we want to find.

Since the plane completes the turn in 20 seconds, we can use the formula:

v = s/t

where t is the time taken (20 seconds in this case).

Solving for s, we get:

s = v*t = 200 m/s * 20 s = 4000 m

And solving for r, we get:

r = s/θ = 4000 m / (90 degrees * π/180) = 2222 m

Now we can substitute into the centripetal acceleration formula:

a = v^2/r = (200 m/s)^2/2222 m = 18 m/s^2

Therefore, the magnitude of the average acceleration of the plane is 18 m/s^2, which is closest to 14 m/s^2 (option D).

Question 8

A cannon fires a projectile as shown.The dashed line shows the trajectory in the absence of gravity; points MNOP correspond to the position of the projectile at one second intervals.If g = 10 m/s², the lengths X,Y,Z are:

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Question 9

A ball is thrown horizontally from the top of a 20-m high hill.It strikes the ground at an angle of 45°.With what speed was it thrown? Use g = 10 m/s².

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Question 10

An airplane is flying north at 500 km/h.It makes a gradual 180° turn at constant speed, changing its direction of travel from north through east to south.The process takes 40 s.The average acceleration of the plane for this turn is:

Accepted Answer

The average acceleration can be calculated using the change in velocity over time. The plane changes its velocity direction from north to south, maintaining the same speed. The magnitude of the velocity change is twice the speed (500 km/h north to 500 km/h south), which is 1000 km/h. Over 40 seconds, the average acceleration is $ \frac{1000 \, \text{km/h}}{40 \, \text{s}} = 25 \, \text{km/h} \cdot \text{s}^{-1} $, directed south because the change in velocity is towards the south.

Question 11

A bullet shot horizontally from a gun:

Accepted Answer

This is because, regardless of its horizontal velocity, the bullet is still subject to the same vertical acceleration due to gravity as the vertically dropped bullet. Therefore, both bullets will hit the ground at the same time.

Question 12

A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s.How long is the stone in the air? Assume that it lands on the ground below the cliff, and that the ground below the cliff is flat.

Accepted Answer

We can use the kinematic equations to solve for the time the stone is in the air. Let's use the following equation:
Δy = v0*t + (1/2)*a*t^2
where Δy is the change in height (59.4 m), v0 is the initial velocity (19.5 m/s), a is the acceleration due to gravity (-9.81 m/s^2), and t is the time. We can rearrange the equation and solve for t:
t = (-v0 ± sqrt(v0^2 - 4*(1/2)*a*Δy))/(2*(1/2)*a)
t = (-19.5 ± sqrt(19.5^2 - 4*(1/2)*(-9.81)*(59.4)))/(2*(1/2)*(-9.81))
t ≈ 5.98 s
Since we're looking for the time the stone is in the air, we'll use the positive solution for time:
t ≈ 5.98 s
So the stone is in the air for approximately 5.98 seconds, which is closest to 6.00 seconds (choice C).

Question 13

A stone thrown from the top of a tall building follows a path that is:

Accepted Answer

The path of a stone thrown from a tall building is best described by a parabolic curve due to the influence of gravity on its trajectory.

Question 14

A dart is thrown horizontally toward X at 20 m/s as shown.It hits Y 0.1 s later.The distance XY is:

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Question 15

A toy racing car moves with constant speed around the circle shown below.When it is at point A its coordinates are x = 0, y = 3m and its velocity is (6 m/s)  .When it is at point B its velocity and acceleration are:

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Question 16

A stone is thrown horizontally and follows the path XYZ shown.The direction of the acceleration of the stone at point Y is:

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Question 17

An object, tied to a string, moves in a circle at constant speed on a horizontal surface as shown.The direction of the displacement of this object, as it travels from W to X is:

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Question 18

The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h.At what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s².

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Question 19

Which of the curves on the graph below best represents the vertical component v_y versus t for a projectile fired at an angle of 45° above the horizontal?

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Question 20

Two projectiles are in flight at the same time.The acceleration of one relative to the other:

Accepted Answer

The acceleration of both projectiles is solely due to gravity, which is a constant 9.8 m/s^2 downwards. Therefore, the acceleration of one relative to the other is zero.

Quiz 4: Motion in Two and Three Dimensions

A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outwards with a speed of 20 m/s.It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10 m/s²

An object is shot from the back of a railroad flatcar moving at 40 km/h on a straight horizontal road.The launcher is aimed upward, perpendicular to the bed of the flatcar.The object falls:

A large cannon is fired from ground level over level ground at an angle of 30° above the horizontal.The muzzle speed is 980 m/s.Neglecting air resistance, the projectile will travel what horizontal distance before striking the ground?

A particle moves at constant speed in a circular path.The instantaneous velocity and instantaneous acceleration vectors are:

A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s.Using g = 10 m/s², the distance from launching to landing points is:

A bomber flying in level flight with constant velocity drops a bomb before it is over the target.Neglecting air resistance, which one of the following is NOT true?

An airplane makes a gradual 90°turn while flying at a constant speed of 200 m/s.The process takes 20.0 seconds to complete.For this turn the magnitude of the average acceleration of the plane is:

A cannon fires a projectile as shown.The dashed line shows the trajectory in the absence of gravity; points MNOP correspond to the position of the projectile at one second intervals.If g = 10 m/s², the lengths X,Y,Z are:

A ball is thrown horizontally from the top of a 20-m high hill.It strikes the ground at an angle of 45°.With what speed was it thrown? Use g = 10 m/s².

An airplane is flying north at 500 km/h.It makes a gradual 180° turn at constant speed, changing its direction of travel from north through east to south.The process takes 40 s.The average acceleration of the plane for this turn is:

A bullet shot horizontally from a gun:

A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s.How long is the stone in the air? Assume that it lands on the ground below the cliff, and that the ground below the cliff is flat.

A stone thrown from the top of a tall building follows a path that is:

A dart is thrown horizontally toward X at 20 m/s as shown.It hits Y 0.1 s later.The distance XY is:

A toy racing car moves with constant speed around the circle shown below.When it is at point A its coordinates are x = 0, y = 3m and its velocity is (6 m/s) .When it is at point B its velocity and acceleration are:

A stone is thrown horizontally and follows the path XYZ shown.The direction of the acceleration of the stone at point Y is: $A stone is thrown horizontally and follows the path XYZ shown.The direction of the acceleration of the stone at point Y is: A) \downarrow B) \leftarrow C) D) E)$

An object, tied to a string, moves in a circle at constant speed on a horizontal surface as shown.The direction of the displacement of this object, as it travels from W to X is:

The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h.At what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s².

Which of the curves on the graph below best represents the vertical component v_y versus t for a projectile fired at an angle of 45° above the horizontal?

Two projectiles are in flight at the same time.The acceleration of one relative to the other:

Quiz 4: Motion in Two and Three Dimensions

A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outwards with a speed of 20 m/s.It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10 m/s2

An object is shot from the back of a railroad flatcar moving at 40 km/h on a straight horizontal road.The launcher is aimed upward, perpendicular to the bed of the flatcar.The object falls:

A large cannon is fired from ground level over level ground at an angle of 30° above the horizontal.The muzzle speed is 980 m/s.Neglecting air resistance, the projectile will travel what horizontal distance before striking the ground?

A particle moves at constant speed in a circular path.The instantaneous velocity and instantaneous acceleration vectors are:

A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s.Using g = 10 m/s2, the distance from launching to landing points is:

A bomber flying in level flight with constant velocity drops a bomb before it is over the target.Neglecting air resistance, which one of the following is NOT true?

An airplane makes a gradual 90°turn while flying at a constant speed of 200 m/s.The process takes 20.0 seconds to complete.For this turn the magnitude of the average acceleration of the plane is:

A cannon fires a projectile as shown.The dashed line shows the trajectory in the absence of gravity; points MNOP correspond to the position of the projectile at one second intervals.If g = 10 m/s2, the lengths X,Y,Z are:

A ball is thrown horizontally from the top of a 20-m high hill.It strikes the ground at an angle of 45°.With what speed was it thrown? Use g = 10 m/s2.

An airplane is flying north at 500 km/h.It makes a gradual 180° turn at constant speed, changing its direction of travel from north through east to south.The process takes 40 s.The average acceleration of the plane for this turn is:

A bullet shot horizontally from a gun:

A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s.How long is the stone in the air? Assume that it lands on the ground below the cliff, and that the ground below the cliff is flat.

A stone thrown from the top of a tall building follows a path that is:

A dart is thrown horizontally toward X at 20 m/s as shown.It hits Y 0.1 s later.The distance XY is:

A toy racing car moves with constant speed around the circle shown below.When it is at point A its coordinates are x = 0, y = 3m and its velocity is (6 m/s) .When it is at point B its velocity and acceleration are:

A stone is thrown horizontally and follows the path XYZ shown.The direction of the acceleration of the stone at point Y is:

An object, tied to a string, moves in a circle at constant speed on a horizontal surface as shown.The direction of the displacement of this object, as it travels from W to X is:

The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h.At what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s2.

Which of the curves on the graph below best represents the vertical component vy versus t for a projectile fired at an angle of 45° above the horizontal?

Two projectiles are in flight at the same time.The acceleration of one relative to the other:

A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outwards with a speed of 20 m/s.It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10 m/s²

A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s.Using g = 10 m/s², the distance from launching to landing points is:

A cannon fires a projectile as shown.The dashed line shows the trajectory in the absence of gravity; points MNOP correspond to the position of the projectile at one second intervals.If g = 10 m/s², the lengths X,Y,Z are:

A ball is thrown horizontally from the top of a 20-m high hill.It strikes the ground at an angle of 45°.With what speed was it thrown? Use g = 10 m/s².

A stone is thrown horizontally and follows the path XYZ shown.The direction of the acceleration of the stone at point Y is: $A stone is thrown horizontally and follows the path XYZ shown.The direction of the acceleration of the stone at point Y is: A) \downarrow B) \leftarrow C) D) E)$

The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h.At what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s².

Which of the curves on the graph below best represents the vertical component v_y versus t for a projectile fired at an angle of 45° above the horizontal?