Question 1

A bullet is fired horizontally with an initial velocity of 300 m/s from a 20-m high tower. If air resistance is negligible, the bullet hits downrange about

Accepted Answer

The answer of A bullet is fired horizontally with an...

Question 2

An object is thrown vertically into the air. In this case air resistance affects motion. Compared with its time for ascent, the time for its descent is

Accepted Answer

When an object is thrown vertically into the air, air resistance affects its motion during both the ascent and the descent. However, since the object is moving against gravity during the ascent, the upward force exerted by air resistance is opposing gravity and slowing down the object. This means that the time for ascent will be longer than it would be without air resistance. During the descent, the object is moving with gravity, and the downward force exerted by air resistance is helping gravity and therefore increasing the object's speed. This means that the time for descent will be shorter than it would be without air resistance. Overall, the time for descent is shorter than the time for ascent.

Question 3

If you throw a stone horizontally from the top of a cliff, one second after leaving your hand its vertical distance below the top of the cliff is

Accepted Answer

The vertical distance a stone falls is determined by the formula $d = \frac{1}{2}gt^2$, where $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$) and $t$ is the time in seconds. For $t = 1$ second, $d = \frac{1}{2} \times 9.8 \times 1^2 = 4.9 \, \text{m}$, which is approximately $5 \, \text{m}$.

Question 4

Two projectiles are fired from ground level at equal speeds but different angles. One is fired at an angle of 30° and the other at 60°. Neglecting air resistance, the projectile to hit the ground first will be the one fired at

Accepted Answer

The time taken for a projectile to hit the ground is determined by the vertical component of its velocity. The vertical component of velocity is given by Vsinθ, where V is the initial velocity and θ is the angle of projection. Since the projectiles are fired at equal speeds, the projectile with a smaller angle of projection (θ=30°) will have a larger vertical component of velocity compared to the one fired at a larger angle (θ=60°). Therefore, the projectile fired at 30° will hit the ground before the other projectile.

Question 5

A bullet fired horizontally from a rifle begins to fall

Accepted Answer

The bullet fired horizontally from a rifle will fall as soon as it leaves the barrel due to the force of gravity acting on it. Air friction may affect its trajectory, but it does not cause it to fall. Therefore, choice A is the best option.

Question 6

An Earth satellite is simply a projectile

Accepted Answer

An Earth satellite is a projectile that is in orbit around Earth, which means that it is continually falling towards the planet as it travels forward at a high speed. However, the Earth's curvature keeps the satellite in a stable orbit, so it doesn't crash into the planet.

Question 7

Planets would crash into the Sun if it weren't for

Accepted Answer

The tangential velocities of planets keep them in stable orbits around the Sun, preventing them from crashing into it.

Question 8

Hang time is the time your feet are off the ground in a jump. If you jump upward inside a moving vehicle, your hang time will be

Accepted Answer

Your hang time will be the same as the gravity acting on you will not change regardless of the vehicle's motion. Your upward velocity and the time you spend in the air will depend on the force of your jump, which is independent of the vehicle's motion.

Question 9

A projectile is launched vertically upward at 50 m/s. If air resistance is negligible, its speed upon returning to its starting point is

Accepted Answer

When a projectile is launched vertically upward, its initial velocity is only acting against gravitational acceleration (g). Therefore, the projectile slows down until it reaches its maximum height (where its velocity becomes zero). After that, the projectile starts to fall back to its starting point under the influence of gravity. However, the gravitational acceleration remains the same and in the same direction. Therefore, the velocity of the projectile increases as it falls back to the starting point.

Since air resistance is negligible in this scenario, there is no external force acting on the projectile during its trajectory. Therefore, the projectile should return to its original height with the same speed (magnitude) as it had when it was launched. Thus, the speed upon returning to its starting point is the same as the initial velocity, which is 50 m/s.

Question 10

When air drag affects the motion of projectiles, they don't travel

Accepted Answer

Air drag, also known as air resistance or friction, works against the motion of projectiles by decreasing their speed and altering their trajectory. As a result, projectiles don't travel as high or as far as they would without air drag. Therefore, both choices A and B are correct.

Question 11

A projectile is launched vertically upward at 50 m/s. If air resistance does affect motion, then its speed upon returning to its starting point is

Accepted Answer

When a projectile is launched vertically upward with a certain initial velocity, it slows down as it moves upward against the force of gravity until it reaches its highest point where its velocity becomes zero. On its way back down, it gains speed due to gravity. However, if air resistance affects its motion, it will slow down during its ascent and have less velocity when it reaches its highest point than it would in the absence of air resistance. This means that when it returns to its starting point, its speed will also be less than its initial velocity of 50 m/s. Therefore, the best choice is A - less than 50 m/s.

Question 12

The tangential velocity of an Earth satellite is its velocity

Accepted Answer

The tangential velocity of an Earth satellite is its velocity parallel to the surface of Earth, which means it is moving along a path that is tangential to the Earth's surface at any given point in its orbit.

Question 13

The radial velocity of an Earth satellite is its velocity

Accepted Answer

The radial velocity of an Earth satellite is the component of its velocity that is perpendicular to the surface of the Earth. It is called radial because it points towards or away from the center of the Earth.

Question 14

Ideally, a ball is thrown up at an angle and lands downrange. Because of air resistance, the distance reached is

Accepted Answer

Air resistance acts upon the ball during its flight, slowing it down and reducing its range compared to a theoretical perfect ball with no air resistance. Therefore, the distance reached by the ball will be less than if it were thrown in a vacuum or in negligible atmospheric conditions.

Question 15

A ball player wishes to determine pitching speed by throwing a ball horizontally from an elevation 5 m above ground level. The ball lands 20 m downrange. The player's pitching speed is about

Accepted Answer

The horizontal velocity of the ball remains constant during its flight, and since there is no vertical acceleration (assuming air resistance is negligible), the vertical velocity can be ignored. Thus, the motion of the ball can be treated as a projectile motion problem, and we can use the following kinematic equations:

Δx = Vx * t
Δy = 1/2 * g * t^2

where Δx = 20 m, Δy = -5 m (since the ball lands at the same height as it was thrown from), Vx is the horizontal velocity (which we want to find), g is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight.

Using the first equation to solve for t, we get:

t = Δx / Vx

Substituting this into the second equation, we get:

Δy = 1/2 * g * (Δx / Vx)^2

Solving for Vx, we get:

Vx = Δx / sqrt(2Δy / g)

Plugging in the given values, we get:

Vx = 20 / sqrt(2(5) / 9.8) ≈ 20 m/s.

Question 16

It there were no gravity a stone thrown upward at 45 degrees would follow a straight-line path. But because of gravity, at the end of 1 second, the stone is actually

Accepted Answer

The stone falls 5 meters below the straight-line path due to gravity, as the acceleration due to gravity is approximately 9.8 m/s², and using the formula for distance fallen under gravity (d = 0.5 * g * t²), we get d = 0.5 * 9.8 * 1² ≈ 5 m.

Question 17

A gun with a muzzle velocity of 100 m/s is fired horizontally from a tower. Neglecting air resistance, how far downrange will the bullet be 1 second later?

Accepted Answer

Since the bullet is fired horizontally, there is no initial vertical velocity. Therefore, the only motion is in the horizontal direction. In one second, the bullet will travel a distance equal to the product of its velocity and the time traveled. Therefore, the distance downrange is:
distance = velocity x time = 100 m/s x 1 s = 100 m
Therefore, the answer is C, 100 m.

Question 18

The paths of fragments of fireworks are

Accepted Answer

Fireworks fragments follow parabolic paths due to the force of gravity acting on them once they are launched into the air. This is similar to the path of a projectile, which is also affected in the same way by gravity. Therefore, option C is also incorrect. Option A is not always true, as the trajectory of a firework can be affected by wind or other external factors, causing it to veer off course.

Question 19

While an airplane flies at 40 m/s at an altitude of 500 meters, the pilot drops a heavy package that falls to the ground. Neglecting air drag, about where does the package land relative to the plane flying above?

Accepted Answer

Since the package is dropped from the airplane without any lateral force, both objects (plane and package) will follow the same parabolic path. In other words, the horizontal distance between them remains constant throughout the drop. Therefore, the package will land directly beneath the plane.

Question 20

The Moon does not crash into Earth because

Accepted Answer

The Moon does not crash into Earth because it has a sufficient tangential speed, meaning it is moving fast enough sideways to not fall into Earth's gravitational pull. Earth's gravitational field is strong enough to keep the Moon in orbit, but the Moon's tangential speed keeps it in a stable orbit instead of crashing into Earth. The gravitational pull of other planets is not a significant factor in keeping the Moon in orbit around Earth. The mass of the Moon compared to Earth also plays a role in the stability of the system, but it is not the main reason that the Moon does not crash into Earth.

Quiz 10: Projectile and Satellite Motion