# Worksheet: Parabolic Trajectories

In this worksheet, we will practice calculating the properties of the motion of a projectile moving under constant acceleration due to gravity.

**Q5: **

A daredevil is attempting to jump his motorcycle over a line
of buses parked end to end by driving up a
ramp at a speed
of
50.0 m/s.
Each bus is 22.0 m long,
and the top of the take-off ramp is at the same height as the top of the buses.
Assume that the acceleration due to gravity is
9.8 m/s^{2}
and that air resistance is negligible.
How many buses can he clear?

**Q6: **

At a particular instant, a hot-air balloon is m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl in the hot-air balloon throws a ball horizontally, relative to herself, with an initial speed of 20.0 m/s. When she lands, what will the horizontal distance between her and the ball be? Ignore air resistance.

**Q15: **

An astronaut stands on a wide, flat piece of ground on the planet Mars. The astronaut kicks a soccer ball, giving the ball an initial velocity of 15 m/s at an angle of above the horizontal. Use a value of 3.7 m/s^{2} for the acceleration of gravity on Mars.

What is the horizontal displacement from the point where the ball is kicked to the point where the ball lands?

An identical ball is given an identical kick by an astronaut on a wide, flat surface of ground on the Moon. Gravitational acceleration by the moon is one-sixth of that on Earth. What is the horizontal displacement from the point where the ball is kicked to the point where the ball lands?

**Q16: **

A man throws a rock from the edge of a cliff that has a height of m. The rock is thrown with an initial speed of 30 m/s at an angle of above the horizontal. Assume that vertical displacement above the clifftop corresponds to positive values.

What is the maximum vertical displacement of the rock from the clifftop?

What is the horizontal distance of the rock from the clifftop when the rock has its maximum vertical upward displacement?

How much time passes between the rock being released from the man’s hand and the rock hitting the ground?

What is the horizontal distance of the rock from the clifftop when the rock hits the ground?

What is the vertical displacement of the rock from the clifftop at the time ?

What is the vertical displacement of the rock from the clifftop at the time ?

What is the vertical displacement of the rock from the clifftop at the time ?

**Q17: **

A projectile is launched at an angle of from the horizontal and lands 20 seconds later at the same height as it was launched from.

What is the initial speed of the projectile?

What is the maximum altitude that the projectile reaches?

What is the horizontal range of the projectile?

Calculate the displacement of the projectile from its launch position to the position on its trajectory 15 seconds after launch.

- A
- B
- C
- D
- E

**Q20: **

You throw a baseball at an initial speed of 12.4 m/s at an angle of above the horizontal. The ball travels a horizontal distance of m. If the acceleration due to gravity was doubled, what would the ball’s initial speed have to be when thrown at the same angle for the ball to travel a distance of m?

**Q21: **

A planet has an acceleration due to gravity of
5.17 m/s^{2}.
On this planet, there is a mountain 19.3 km high that has a
289-km-radius base.
What initial horizontal velocity would be needed
for an object thrown from the mountain’s summit for
the object to land at the mountain’s base? Ignore any
curvature of the planet, assume that the gradient of the mountain is constant,
and assume that the base of the mountain is circular,
with the peak of the mountain
vertically above the center of the circle.

**Q24: **

MIT’s robot cheetah can jump over obstacles. The robot has a maximum speed of 12.0 km/h.

The robot is moving at its maximum speed and jumps at an angle above the horizontal. What is the maximum height the robot reaches?

The robot is moving at its maximum speed and jumps, reaching a maximum height of 47 cm. At what angle above the horizontal did the robot launch itself?