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In this lesson, we will learn how to calculate the properties of the motion of a projectile moving under constant acceleration due to gravity.

Q1:

A bullet is shot horizontally with a speed of 2 . 0 × 1 0 2 m/s from a height of 1.5 m.

How much time elapses before the bullet hits the ground?

How far does the bullet travel horizontally?

Q2:

On the surface of the planet Arcon, the maximum possible horizontal range of a projectile launched with a speed of 14 m/s is 25 m. What is the acceleration due to gravity on Arcon?

Q3:

A dart is thrown horizontally at a speed of 10 m/s at the bull’s-eye of a dartboard 2.4 m away.

How far below the intended target does the dart hit?

Q4:

An eagle is flying horizontally at a speed of 4.00 m/s when a fish in its talons wiggles loose and falls into the lake 9.00 m below. Calculate the speed of the fish relative to the water when it hits the water. Use a value of 9.80 m/s^{2} for the 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 2 8 ∘ 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 1 . 0 × 1 0 2 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.

Q7:

An aircraft is coming in for a landing at 300 meters height when its propeller falls off. The aircraft is flying at 40.0 m/s horizontally. Neglecting air resistance, with what translational velocity does the propeller hit the ground?

Q8:

An athlete can jump a horizontal distance of 8.0 m in the broad jump. What is the maximum horizontal distance the athlete can jump on the Moon, where the gravitational acceleration is one-sixth that of Earth? Give your answer to two significant figure precision.

Q9:

Drew Brees of the New Orleans Saints throws a football at a speed of 22.5 m/s. He angles the throw direction at 1 0 ∘ above the horizontal. What distance does the football travel horizontally if it is to be caught at the same height at which it was thrown?

Q10:

In 1999, Robbie Knievel was the first person to ever jump the Grand Canyon on a motorcycle. Knievel jumped a 69 m horizontal distance, taking off from the ramp at 35.8 m/s. What angle above the horizontal was the ramp inclined at?

Q11:

An artillery shell is fired vertically upward at a target 200 m vertically above the ground. When the shell is 100 m above the ground, it has a speed of 100 m/s. What is the speed of the shell when it hits its target? Neglect drag forces on the shell.

Q12:

A mountain biker encounters a jump on a race course that sends his bike into the air at an angle 6 0 ∘ above the horizontal. The bike lands at a point 45 m horizontally and 20 m vertically downward away from its launch point. What is the bike’s initial speed?

Q13:

A golfer on a fairway is 0.070 km away from the green, which sits below the level of the fairway by 20.0 m. The golfer hits the ball at an angle of 4 0 ∘ from the horizontal with an initial speed of 2 . 0 × 1 0 4 cm/s, at what distance from the green will the ball land?

Q14:

A soccer ball that scores a goal hits the net 2.44 m above the ground. A player kicks the ball at a distance of 10 m from the goal at an angle of 2 5 ∘ above the horizontal. What is the initial speed of the soccer ball?

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 4 5 ∘ 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 1 . 0 × 1 0 2 m. The rock is thrown with an initial speed of 30 m/s at an angle of 5 3 ∘ 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 𝑡 = 2 . 0 s ?

What is the vertical displacement of the rock from the clifftop at the time 𝑡 = 4 . 0 s ?

What is the vertical displacement of the rock from the clifftop at the time 𝑡 = 6 . 0 s ?

Q17:

A projectile is launched at an angle of 3 0 ∘ 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.

Q18:

A crossbow is aimed horizontally at a target 27 m away. The crossbow’s bolt hits the target 12 cm below the spot at which it is aimed. What was the initial horizontal velocity of the bolt?

Q19:

A basketball player shoots toward a basket that is 5.5 m away horizontally and 2.6 m away vertically. The ball is released 1.4 m above the floor at an angle of 6 4 ∘ above the horizontal. What must the initial speed of the basketball be for it to hit the basket?

Q20:

You throw a baseball at an initial speed of 12.4 m/s at an angle of 2 3 . 6 ∘ above the horizontal. The ball travels a horizontal distance of 𝑑 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 𝑑 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 centre of the circle.

Q22:

A marble rolls off a table top 1.3 m high and hits the floor at a point that is horizontally 2.4 m away from the table’s edge.

For how much time is the marble in the air?

What is the speed of the marble when it leaves the table’s edge?

What is the speed of the marble when it hits the floor?

Q23:

In a volcanic eruption, a rock was launched from the crater of a volcano at an angle of 4 2 . 1 ∘ above the horizontal. The rock landed 762 m below the crater, 1.45 km horizontally distant.

At what speed did the rock leave the crater?

For how much time was the rock airborne?

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 6 0 ∘ 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?

Q25:

A long jumper can jump a distance of 8.0 m when he takes off at an angle of 4 5 ∘ above the horizontal. Assuming he can jump with the same initial speed at all angles, how much is his horizontal displacement in a jump reduced by taking off at an angle 3 0 ∘ rather than 4 5 ∘ above the horizontal?

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