Question 1

Which of the following statements are true about an object in two-dimensional projectile motion with no air resistance? (There could be more than one correct choice. )

Accepted Answer

The acceleration of an object in two-dimensional projectile motion with no air resistance is constant and directed downward due to gravity. This means the horizontal acceleration is always zero (since there is no air resistance to slow the object down horizontally), and the vertical acceleration is always $g$ (9.8 m/s$^2$ downward), making statement E correct.

Question 2

Mary and Debra stand on a snow-covered roof.They both throw snowballs with the same initial speed,but in different directions.Mary throws her snowball downward,at 30° below the horizontal;Debra throws her snowball upward,at 30° above the horizontal.Which of the following statements are true about just before the snowballs reach the ground below? (There could be more than one correct choice. )

Accepted Answer

A) Debra's snowball, thrown upward, will take longer to hit the ground because it first has to rise to its peak before falling down, effectively taking a longer path and time compared to Mary's snowball which is thrown downward from the start. D) Both snowballs are subject to Earth's gravity, which means they both have the same acceleration due to gravity, regardless of their initial direction of motion.

Question 3

In an air-free chamber,a pebble is thrown horizontally,and at the same instant a second pebble is dropped from the same height.Compare the times of fall of the two pebbles.

Accepted Answer

Both pebbles fall under the same acceleration due to gravity, and since air resistance is not a factor in an air-free chamber, they will both hit the ground at the same time, regardless of their horizontal or vertical motion. Therefore, they hit at the same time.

Question 4

A ball thrown horizontally from a point 24 m above the ground,strikes the ground after traveling horizontally a distance of 18 m.With what speed was it thrown,assuming negligible air resistance?

Accepted Answer

The time it takes for the ball to hit the ground is determined by its vertical motion. Using the equation $y = \frac{1}{2}gt^2$, where $y = 24$ m and $g = 9.8$ m/s$^2$, we can solve for $t$. Plugging in the values, we get $t = \sqrt{\frac{2y}{g}} = \sqrt{\frac{2 \times 24}{9.8}} \approx 2.2$ s. The horizontal speed $v$ is constant, and since it covers 18 m in 2.2 s, $v = \frac{18}{2.2} \approx 8.18$ m/s, which rounds to 8.1 m/s.

Question 5

A player kicks a soccer ball in a high arc toward the opponent's goal.At the highest point in its trajectory

Accepted Answer

At the highest point in its trajectory, the soccer ball's velocity is not zero; it has a horizontal component of velocity. The acceleration due to gravity (9.8 m/s^2 downward) is also not zero, affecting the ball throughout its flight, including at its highest point.

Question 6

James and John dive from an overhang into the lake below.James simply drops straight down from the edge.John takes a running start and jumps with an initial horizontal velocity of 25 m/s.Compare the time it takes each to reach the lake below if there is no air resistance.

Accepted Answer

Since there is no air resistance, the only force acting on both James and John is gravity, which causes them to accelerate downward at the same rate of 9.8 m/s2. This means that the time it takes for both to reach the surface of the lake will only depend on the height of the overhang, and not on their initial velocities or masses. Therefore, James and John will reach the surface of the lake at the same time.

Question 7

A pilot drops a package from a plane flying horizontally at a constant speed.Neglecting air resistance,when the package hits the ground the horizontal location of the plane will

Accepted Answer

Since there is no air resistance, the package will maintain the same horizontal velocity as the plane. Therefore, when the package hits the ground, the plane will be directly over it.

Question 8

For general projectile motion with no air resistance,the horizontal component of a projectile's velocity

Accepted Answer

The horizontal component of a projectile's velocity remains a non-zero constant because there is no force acting horizontally to change its velocity. As long as there is no external force acting on the projectile, its horizontal velocity will remain constant throughout its motion.

Question 9

Mary and Debra stand on a snow-covered roof.They both throw snowballs with the same initial speed,but in different directions.Mary throws her snowball downward,at 30° below the horizontal;Debra throws her snowball upward,at 30° above the horizontal.Which of the following statements are true about just as the snowballs reach the ground below? (There could be more than one correct choice. )

Accepted Answer

Both snowballs will hit the ground with the same speed because they have the same initial speed and are thrown at the same angle. Mary's snowball reaches the ground before Debra's snowball because it is thrown downward, while Debra's snowball is thrown upward.

Question 10

A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal.If there is no air resistance,what is the speed of the ball when it returns to the same horizontal level?

Accepted Answer

When the ball is thrown, it has a horizontal component of velocity given by Vx = V0cos(theta) = 8.0cos(35) = 6.57 m/s, and a vertical component of velocity given by Vy = V0sin(theta) = 8.0sin(35) = 4.57 m/s (taking upwards as positive).

At the highest point of its trajectory, the vertical component of velocity becomes zero, and the horizontal component remains constant throughout. Therefore, the speed of the ball when it returns to the same horizontal level is equal to the initial horizontal speed, which is 6.57 m/s (or approximately 8 m/s).

Note that gravity does not affect the horizontal component of velocity, so the horizontal speed remains constant. The vertical speed, however, is affected by gravity, which causes it to decrease to zero at the highest point and then increase again in the downward direction.

Question 11

James and John dive from an overhang into the lake below.James simply drops straight down from the edge.John takes a running start and jumps with an initial horizontal velocity of 25 m/s.If there is no air resistance,when they reach the lake below

Accepted Answer

The answer of James and John dive from an overhang...

Question 12

A ball is thrown with an initial velocity of 20 m/s at an angle of 60° above the horizontal.If we can neglect air resistance,what is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

Accepted Answer

At the top of its trajectory, the vertical component of the velocity is zero, but the horizontal component remains constant throughout the motion. The horizontal component is given by $ v_x = v \cdot \cos(\theta) = 20 \cdot \cos(60°) = 10 \, \text{m/s} $.

Question 13

For general projectile motion with no air resistance,the vertical component of a projectile's acceleration

Accepted Answer

In the absence of air resistance, the only force acting on a projectile is gravity, which provides a constant acceleration downwards. This means the vertical component of the projectile's acceleration remains constant and is equal to the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).

Question 14

A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically.Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance?

Accepted Answer

The horizontal velocity of the ball does not affect its vertical velocity, meaning that the ball and the stone will hit the ground at the same time. However, the ball will travel a greater horizontal distance in the same time as the stone since it has a horizontal velocity. Therefore, the ball is traveling faster than the stone when it hits the ground.

Question 15

A boulder rolls off of a very high cliff and experiences no significant air resistance.While it is falling,its trajectory is never truly vertical.

Accepted Answer

The boulder, once it rolls off the cliff, follows a parabolic trajectory due to its initial horizontal velocity combined with the acceleration due to gravity acting on it vertically. This results in a curved path, not a vertical one.

Question 16

For general projectile motion with no air resistance,the horizontal component of a projectile's acceleration

Accepted Answer

The horizontal component of a projectile's velocity remains constant throughout its motion, since there is no external force acting horizontally. Therefore, the acceleration in the horizontal direction must be zero as well, according to Newton's second law (F = ma).

Question 17

A girl throws a rock horizontally,with a velocity of 10 m/s,from a bridge.It falls 20 m to the water below.How far does the rock travel horizontally before striking the water,assuming negligible air resistance?

Accepted Answer

The horizontal motion of the rock is independent of its vertical motion. Therefore, we can use the formula d = vt, where d is distance, v is the velocity, and t is time. In this case, we are trying to find d, so we need to rearrange the formula to solve for t: t = d/v. We know v = 10 m/s and we want to find t when the rock hits the water, so we can use the vertical motion formula h = 1/2gt^2, where h is the height (20 m) and g is the acceleration due to gravity (9.8 m/s^2). Solving for t, we get t = sqrt(2h/g) = sqrt(40/9.8) = 2.02 s (rounded to two decimal places). Now we can use the horizontal motion formula to find the distance traveled: d = vt = 10 m/s x 2.02 s = 20.2 m (rounded to one decimal place). Therefore, the answer is C) 20 m.

Question 18

A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff.A stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s.What is the height of the cliff if air resistance is negligibly small?

Accepted Answer

We can use the following kinematic equation to solve for the height of the cliff:
h = vi^2/2g
where h is the height of the cliff, vi is the initial velocity (which is the horizontal velocity of the stone), and g is the acceleration due to gravity.

First, we need to find the time it takes for the stone to hit the ground. Since the stone is thrown horizontally, its vertical velocity is 0 m/s. We can use the following kinematic equation to solve for the time it takes for the stone to hit the ground:
y = viy*t + (1/2)gt^2
where y is the height of the cliff, viy is the initial vertical velocity (which is 0 m/s), and t is the time it takes for the stone to hit the ground.

Simplifying the equation, we get:
y = (1/2)gt^2

Plugging in the given values, we get:
y = (1/2)(9.8 m/s^2)(4.3 s)^2 = 91.17 m

Therefore, the height of the cliff is approximately 91 m. The best choice is D.

Question 19

The acceleration due to gravity on the Moon is only one-sixth of that on Earth,and the Moon has no atmosphere.If you hit a baseball on the Moon with the same effort (and therefore at the speed and angle)as on Earth,how far would the ball would travel on the Moon compared to on Earth? Neglect air resistance on Earth.

Accepted Answer

The answer of The acceleration due to gravity on the...

Question 20

A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal.It reaches its highest point and starts falling down.Which of the following statements about the rock's motion are true just before it hits the ground? (There could be more than one correct choice. )

Accepted Answer

The horizontal velocity component remains constant throughout the motion in the absence of air resistance.

Quiz 4: Two-Dimensional Kinematics