Question 1

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

The ball's initial velocity (horizontal) can be found using the equation: 
v = d/t 
where v is the horizontal velocity, d is the distance traveled, and t is the time taken.

Since the ball is thrown horizontally, there is no initial vertical velocity, hence we can use: 
d = (1/2)g*t^2 
where g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken for the ball to land.

Combining these equations, we get: 
v = d / (sqrt(2*h/g))
where h is the initial height of the ball (5 m in this case).

Plugging in the values, we get: 
v = 20 / (sqrt(2*5/9.8)) = 20 m/s.

Therefore, the player's pitching speed is 20 m/s.

Question 2

Ignoring air drag, what is the maximum speed that can be given to a horizontally moving tennis ball as it clears the net 1.25 m high to remain within the edge of the court, which is 12.0 m distant?

Accepted Answer

The maximum speed can be calculated using the kinematic equations for projectile motion. The time to reach the net is determined by the vertical motion, and the horizontal distance is covered in this time. Solving these gives the maximum speed as 24.0 m/s.

Question 3

After a rock that is thrown straight up reaches the top of its path and is starting to fall back down, its acceleration is

Accepted Answer

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

Question 4

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 s later?

Accepted Answer

The bullet will continue to travel horizontally at a constant velocity of 100 m/s for 1 second, covering a distance of 100 m downrange.

Question 5

Toss a rock at an angle into the air and it follows a curved path. Its velocity at any instant can be resolved into horizontal and vertical components. Which of these components changes with time, and why?

Accepted Answer

The answer of Toss a rock at an angle into...

Question 6

A bullet fired horizontally hits the ground in 0.5 s. If it had been fired with twice the velocity it would have hit the ground in

Accepted Answer

The time for the bullet to hit the ground is dependent on gravitational acceleration (g) and the height from which it was fired. The horizontal velocity of the bullet does not affect the time taken to hit the ground. Therefore, doubling the velocity would not change the time taken to hit the ground, which will remain 0.5 s.

Question 7

Two motorcycle stunt drivers, one light and the other much heavier, drive their motorcycles up and off an inclined ramp at identical speeds. They both rise in the air and land downrange. Neglecting air drag, the one to attain the greatest height and greatest range is the

Accepted Answer

The maximum height and maximum range reached by an object projected at an angle from a given height doesn't depend on the mass of the object but only on its initial speed and the angle of projection. Therefore, neglecting air drag, the light and heavy drivers will attain the same height and range as they are driving up the ramp at identical speeds.

Question 8

A projectile is launched at an angle of 15° above the horizontal and lands downrange. With no air resistance, what other projection angle for the same speed would produce the same downrange distance?

Accepted Answer

For a given launch speed, the range of a projectile launched in a vacuum (ignoring air resistance) is the same for two angles that add up to 90 degrees. Since the given angle is 15 degrees, the complementary angle that would give the same range is 75 degrees (90 - 15 = 75).

Question 9

A projectile is thrown into the air at an angle of 50° and lands on a target that is at the same level the projectile started. With no air resistance it will also land on the target if it is thrown at an angle of

Accepted Answer

The correct answer is A because the projectile will have the same range at angles of 50° and 40°.

Question 10

Tangential velocity is velocity

Accepted Answer

Tangential velocity is the component of velocity that is parallel to the surface of the Earth, especially in the context of circular motion.

Question 11

A hunter aims a rifle at an angle of 10° above the horizontal. The hunter fires a bullet while simultaneously dropping another bullet from the side of the rifle. Which bullet hits the ground first?

Accepted Answer

Both bullets will experience the same acceleration due to gravity, so the vertical displacement of both bullets will be the same. However, the fired bullet will also have a horizontal velocity, causing it to travel farther before hitting the ground. Therefore, the dropped bullet will hit the ground first.

Question 12

A hunter aims a rifle at an angle of 10° below the horizontal. The hunter fires a bullet while simultaneously dropping another bullet from the side of the rifle. Which bullet hits the ground first?

Accepted Answer

Both bullets experience the same acceleration due to gravity, regardless of their initial velocities. The fired bullet has some initial horizontal velocity, which means it will take longer to reach the ground than the dropped bullet, which falls vertically. Therefore, the dropped bullet hits the ground first, making choice A the incorrect answer. Since only one of the statements is true, C (both hit at the same time) is also incorrect. Therefore, the correct answer is B, the fired one.

Question 13

An airplane flies at 40 m/s at an altitude of 50 m. The pilot drops a heavy package, which falls and strikes the ground. Neglecting air resistance, where does the package land?

Accepted Answer

The answer of An airplane flies at 40 m/s at...

Question 14

An Earth satellite is simply a projectile freely falling around the Earth.

Accepted Answer

An Earth satellite is essentially a projectile that is continuously falling around the Earth due to the gravitational pull of the Earth. This means that the satellite is in a state of free fall and is not being pulled towards the Earth's surface by a force other than gravity. Therefore, it can be considered a projectile freely falling around the Earth.

Question 15

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

Accepted Answer

Planets have tangential velocities, which are their velocities perpendicular to the direction of the Sun's gravitational pull. This tangential velocity keeps them from being pulled directly into the Sun and allows them to orbit it instead.

Question 16

Two projectiles are fired at equal speeds but different angles. One is fired at an angle of 30° and the other at 60°. With no air resistance, the projectile to hit the ground first will be the one fired at

Accepted Answer

Both projectiles will have the same initial speed and will experience the same acceleration due to gravity, therefore the only factor to consider is the initial angle of elevation. 
The projectile fired at 30° will have both a horizontal and vertical component of velocity while the one fired at 60° will have a larger vertical component and a smaller horizontal component. The vertical component of velocity determines the time of flight and the maximum height reached by the projectile, while the horizontal component determines the range. 
Since the projectiles have the same initial speed, the one fired at 30° will have a larger horizontal component and therefore a larger range, but it will also have a smaller vertical component and a shorter time of flight. This means that it will hit the ground first than the one fired at 60°, which will spend more time in the air due to its larger vertical component of velocity. Therefore, the correct choice is A)30°.

Question 17

The hang time of an athlete who moves horizontally 2.0 m during a 1.25-m-high jump is

Accepted Answer

The answer of The hang time of an athlete who...

Question 18

Shoot a cannonball horizontally from a cannon at the top of a mountain and it gains speed as it falls and hits the ground below. But fire the cannonball fast enough for circular orbit and no change in speed occurs. Why?

Accepted Answer

The answer of Shoot a cannonball horizontally from a cannon...

Question 19

A ball is thrown horizontally from the top of a tall cliff. Three seconds later, the ball has fallen a vertical distance of

Accepted Answer

Assuming no air resistance, the horizontal speed of the ball remains constant throughout its trajectory. Therefore, the only force acting on the ball is gravity, which causes it to accelerate vertically downwards at a rate of 9.8 m/s^2. 
Using the formula d = 1/2 gt^2, where d is the distance fallen, g is the acceleration due to gravity, and t is the time elapsed, we can calculate the distance fallen by the ball after 3 seconds as:

d = 1/2 (9.8 m/s^2) (3 s)^2 = 44.1 m

Therefore, the ball has fallen a vertical distance of approximately 45 m.

Question 20

For the astronauts inside an orbiting space vehicle, there is no force of Earth's gravity acting on them. This statement is

Accepted Answer

The answer of For the astronauts inside an orbiting space...

Quiz 4: Gravity, Projectiles, and Satellites