Question 1

An object is thrown vertically into the air.Because of air resistance,the time for its descent will be

Accepted Answer

Air resistance will slow down the object on its way down, meaning that the descent time will be longer than the ascent time.

Question 2

Acceleration due to gravity on the moon is less than on Earth,and the moon is smaller than Earth.So compared to an Earth satellite,a satellite in close orbit about the moon would travel

Accepted Answer

A satellite in close orbit about the moon would travel slower because the gravitational force is weaker due to the moon's smaller mass and lower gravity compared to Earth. This results in a lower orbital speed needed to maintain a stable orbit.

Question 3

A ball player wishes to determine pitching speed by throwing a ball horizontally from an elevation of 5 m above the ground.The player sees the ball land 20 m down range.What is the player's pitching speed?

Accepted Answer

First, we must convert the given measurements into SI units. 5 m elevation becomes the initial vertical displacement (y0) of the ball and 20 m distance becomes the horizontal displacement (x). The acceleration of the ball is due to gravity, which is approximately 9.81 m/s^2.

We can use the kinematic equation for horizontal motion:

x = v0xt

where v0x is the initial horizontal velocity and t is the time it takes for the ball to travel 20 m assuming a constant acceleration of 0 m/s^2 in the horizontal direction. Solving for time:

t = x / v0x

For the vertical motion, we can use the kinematic equation:

y = y0 + v0y t + 1/2 a t^2

where v0y is the initial vertical velocity (0 since the ball is thrown horizontally) and y is the final vertical displacement, which is also 0 as the ball lands on the ground. Solving for v0x:

v0x = x / t

Using the time expression derived earlier:

v0x = x / (x / v0x)

v0x^2 = x * g

v0x = sqrt(x * g)

Plugging in the given values:

v0x = sqrt(20 m * 9.81 m/s^2) ≈ 19.8 m/s

Rounding to the nearest 10, the answer is approximately 20 m/s, which is choice C.

Question 4

A river 100 m wide flows due south.A boat that goes 1 m/s relative to the water is pointed due east as it crosses from the west bank.The boat crosses in

Accepted Answer

The answer of A river 100 m wide flows due...

Question 5

The tangential velocity of an Earth satellite is its velocity

Accepted Answer

The tangential velocity of an Earth satellite is parallel to the surface of the Earth, as it moves along its orbital path.

Question 6

An airplane flies at 40 m/s at an altitude of 50 meters.The pilot drops a heavy package which falls to the ground.Where,approximately,does the package land relative to the plane's new position?

Accepted Answer

Assuming no air resistance, the horizontal velocity of the package remains the same as that of the plane, i.e., 40 m/s. However, the vertical velocity of the package is given by v = gt, where g is the acceleration due to gravity (9.8 m/s^2) and t is the time. Using the formula h = 1/2 gt^2 to find the time taken for the package to hit the ground, we get t = sqrt(2h/g) = sqrt(2*50/9.8) = 3.19 seconds (rounded to two decimal places). In this time, the plane would have traveled a horizontal distance of 40 m/s x 3.19 s = 127.6 meters. Therefore, the package would land beneath the plane, or at most, a negligible distance behind it (depending on how high above the ground the package was released). Hence, the answer is A) beneath the plane.

Question 7

A projectile is fired vertically from the surface of the Earth at 8 km/s.The projectile will

Accepted Answer

The velocity of 8 km/s is less than the Earth's escape velocity of approximately 11.2 km/s, so the projectile will rise and then fall back to the Earth's surface.

Question 8

A river 100 m wide flows due south.A boat that goes 1 m/s relative to the water is pointed due east as it crosses from the west bank.Relative to the Earth,the boat travels

Accepted Answer

The boat's velocity relative to the water is 1 m/s due east. The river's velocity relative to the Earth is 1 m/s due south. The boat's velocity relative to the Earth is the vector sum of these two velocities, which is 1 m/s due southeast. The boat travels 100 m due east and 100 m due south, for a total distance of 141 m.

Question 9

Without air resistance,a projectile fired horizontally at 8 km/s from atop a mountain would

Accepted Answer

A projectile fired horizontally at 8 km/s would indeed accelerate downward at g due to gravity, trace a curve matching Earth's curvature, and return to its starting position, repeating its motion, effectively becoming a satellite in orbit.

Question 10

A river 100 m wide flows due south at 1 m/s.A boat that goes 1 m/s relative to the water leaves the west bank.To land at a point due east of its starting point,the boat must be pointed

Accepted Answer

The answer of A river 100 m wide flows due...

Question 11

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

The horizontal distance traveled by the bullet is determined by its horizontal velocity and the time of travel. Since the muzzle velocity is 100 m/s and the bullet is fired horizontally, it will travel 100 meters in 1 second.

Question 12

If a satellite's radial velocity is zero at all times,its orbit must be

Accepted Answer

Radial velocity refers to the speed of an object towards or away from the center of its orbit. If a satellite's radial velocity is zero at all times, then its distance from the center of the orbit must remain constant. This only occurs in a circular orbit, where the satellite maintains a constant distance from the center around the entire orbit. In a parabolic or elliptical orbit, the satellite's distance from the center constantly changes, resulting in a non-zero radial velocity. A geosynchronous orbit is a specific type of circular orbit, but the given information does not provide enough details to determine if the satellite is in a geosynchronous orbit.

Question 13

The radial velocity of an Earth satellite is its velocity

Accepted Answer

The radial velocity of an Earth satellite is its velocity perpendicular to the surface of the Earth, which is directed towards the center of the Earth. This is because the satellite's motion is primarily governed by the gravitational pull of the Earth, which acts towards the center of the Earth. The velocity components parallel to the surface of the Earth are tangential velocity and are not considered as radial velocity.

Question 14

A projectile is fired into the air at an angle of 50 degrees with the ground and lands on a target that is at the same level at which the projectile started.It will also land on the target if it is fired at an angle of

Accepted Answer

The answer of A projectile is fired into the air...

Question 15

The ground speed of an airplane that has an airspeed of 200 km/h when it is in a 200-km/h crosswind is

Accepted Answer

The ground speed of the airplane will be the vector sum of its airspeed and the crosswind. Using the Pythagorean theorem, we have:
ground speed = sqrt((airspeed)^2 + (crosswind)^2)
ground speed = sqrt((200 km/h)^2 + (200 km/h)^2)
ground speed = sqrt(2(200 km/h)^2)
ground speed = sqrt(2) * 200 km/h
ground speed = 283 km/h (rounded to the nearest whole number)

Question 16

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

Accepted Answer

Planets have tangential velocities that move them sideways as they orbit around the sun, balancing the force of gravity pulling them toward the sun. Without their tangential velocities, they would be pulled directly into the sun.

Question 17

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

Accepted Answer

The projectile fired at 30 degrees will have a shorter time of flight because it has a lower vertical component of velocity compared to the one fired at 60 degrees.

Question 18

After a rock thrown straight up reaches the top of its path and then falls a short distance,its acceleration is (neglect air resistance)

Accepted Answer

The acceleration due to gravity is constant and acts downward throughout the motion, including at the top of the path and during the fall.

Question 19

A river 100 m wide flows due south at 1 m/s.A boat that goes 1 m/s relative to the water is pointed due east as it crosses from the west bank.The boat reaches the east bank

Accepted Answer

Since the boat is going due east, it is going perpendicular to the direction of the river flow. Therefore, the boat's velocity relative to the ground is the vector sum of its velocity relative to the water and the river's velocity relative to the ground. Using the Pythagorean theorem, we can find the magnitude of the boat's velocity relative to the ground:
sqrt((1 m/s)^2 + (1 m/s)^2) = sqrt(2) m/s
Since the boat is only traveling east and not south, we can ignore the southward velocity of the river. Therefore, the boat travels 1 m/s east relative to the ground, which means it travels 100 m in 100 seconds. During this time, the boat also experiences a southward motion due to the river's flow. In 100 seconds, the boat would have been carried 100 m south by the river's flow. Therefore, the boat arrives at a point that is 100 m farther south than where it started.

Question 20

A bullet is fired horizontally with an initial velocity of 300 m/s from a tower 20 m high.If air resistance is negligible,the horizontal distance the bullet travels before hitting the ground is about

Accepted Answer

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

Quiz 10: Projectile and Satellite Motion