# Vertical Motion and Free Fall Practice Problems

The operation of a winch is divided into three successive stages: acceleration period (a_{1 }= +0.50 m/s^{2}), constant speed period (v = 2.5 m/s), and deceleration period (a_{3 }= - 0.50 m/s^{2}). A worker uses the winch to pull vertically stacked crates from the ground level. Determine the time required to pull a crate 45 meters.

An insect escaping a predator attack produces a straight vertical acceleration of 400 m/s^{2} over an extremely brief distance of 2.0 cm. What is the maximum height reached by the insect during its escape maneuver? Ignore air resistance.

The vertical ascent phase of a 2500 kg space shuttle lasts 26 s. During this phase, the engine of the space shuttle provides a constant acceleration of 15 m/s^{2}. At t = 26 s, the engine fails. Neglect the effect of resistive forces. Determine the maximum height attained by the space shuttle.

During a voluntary vertical take-off, a dronefly of mass 20 g produces a constant acceleration by flipping its wings for 1.2 s. At t = 1.2 s, the dronefly stops flipping its wings, and 0.2 s later, it is 3.2 m above the take-off level. Calculate the acceleration produced during the first 1.2 s.

A coconut is thrown vertically upward with a speed of 15 m/s from the top of a coconut palm, 3.5 m above the ground. Determine the velocity of the coconut when it strikes the ground.

A diver awaiting his turn to jump from a bridge awkwardly dropped his mobile phone. Initially, the mobile phone is located 7.0 m above the river's surface. At the river's surface, the mobile phone has an impact speed of v. Assume that the mobile phone continues its motion vertically downward with a steady speed of v until it reaches the ground at the bottom of the river. The time taken to reach the bottom of the river, measured from the instant that the phone was dropped, is 6.0 s. Determine the river's water level.

A tennis ball is released without an initial speed from the top of a skyscraper. The height of the skyscraper is 830 m. At the instant the ball was released, a drone located in the same position as the ball was moving vertically downward with a speed of 23 m/s. Determine the speed of the ball when it catches the drone.

An experimental setup is used to create calcium alginate spheres by allowing an alginate solution droplet to fall from the tip of a syringe into a CaCl_{2} bath solution. The droplet strikes the bath solution 0.25 s later. Determine the velocity of the droplet just before striking the bath solution.

The silicon oil droplet motion is investigated during a free fall experiment. A spherical-shaped droplet is established at the end of a syringe's needle tip. The droplet released without initial speed hits the ground after 0.85 s. Determine the distance separating the tip from the ground.

A hot air balloon released from rest in a meadow moves vertically upward with a steady acceleration. After 9 seconds of motion, a stone stuck on the bottom of the basket goes down and strikes the meadow 7 seconds later. Calculate the acceleration of the hot air balloon.

How can a spacecraft change i) its direction or ii) decelerate far out in space where there isn't much matter floating around?

An expeditionary rocket uses 200 kg of fuel per hour. This burned fuel is ejected from the exhaust with a velocity of 2500 km/h relative to the rocket. Find the thrust of the rocket.

A Zeppelin balloonist, moving up with a uniform speed of 10.0 m/s, drops a bag of small rocks at an instant when the balloon is 50.0 m above the ground. What is the maximum height above the ground that the bag attains? (After the bag is dropped, it is under free fall.)

A Montgolfier balloonist, moving up with a uniform speed of 10.0 m/s, drops a bag of stones at an instant when the balloon is 50.0 m above the ground. What is the speed and position of the bag at 0.50 s after its release? After the bag is dropped, it is under free fall.

A moon lander is a spacecraft intended to land on the surface of the moon. When the lander is 15.0 m above the surface, the engine is cut off and has a speed of 1.0 m/s in the downward direction. Also, when the engine is off, the lander is freely falling under the gravity of the moon. What is the landing speed of the lander just before it reaches the surface? Consider the acceleration due to gravity on the surface of the moon as 1.6 m/s^{2}.

A small rock is thrown directly upward with an initial speed of X m/s from the ground. What is the acceleration while the rock is (i) going downward? (ii) going upward? (iii) At the topmost point? Neglect resistance of air.

A stone is thrown directly upward with an initial speed of 10.0 m/s from the ground. When is the velocity of the stone zero? Ignoring resistance of air.

A projectile is thrown vertically upward from the ground with an initial speed of 98.1 m/s. Find the time at which it comes to the same position. Neglect the air resistance.

At the beginning of a basketball match, the basketball is thrown vertically upward by the referee at an initial speed of 19.62 m/s. Find out the time at which the ball is moving at a velocity of 9.81 m/s. Neglect the air resistance.

A player hits a tennis ball with his racket directly upward from the top of a cliff of height 50.0-m. The tennis ball passes him on its way down and passes a point 40.0 m below the point, where the tennis ball left the racket 6.00 s after it was hit. If air resistance is negligible, then what is its acceleration at the highest point?

A man throws a stone vertically upward from the top of a tall building of height 50.0-m. The stone passes him on its way down and passes a point 40.0 m below the point, where the stone left the man's hand 6.00 s after it was thrown. If air resistance is negligible, then what is its speed at the highest point of its journey?

A ball is thrown vertically upward from the top of a tower of a height of 50.0 m. The ball passes him on its way down and passes a point 40.0 m below the point, where the ball left the thrower's hand 6.00 s after it was thrown. If air resistance is negligible, then what is the maximum height reached by it above its starting point?

A person kicks a football vertically upward from the edge of a cliff of height 50.0-m. The football passes him on its way down and passes a point 40.0 m below the point, where the football left the foot of the person, 6.00 s after it was thrown. If air resistance is negligible, then what is the initial speed of the football?

A spacecraft of mass 10,000-kg, initially at rest, is launched vertically with an upward acceleration of 10.0 m/s^{2}. At an altitude of 500 m, the engine of the spacecraft cuts off. What is the speed with which it will be moving just before crashing down to earth's surface?

A rocket of mass 10,000-kg, initially at rest, is fired vertically with an upward acceleration of 10.0 m/s^{2}. At an altitude of 500 m, the engine of the rocket cuts off. What is the maximum altitude it achieves?

A bullet is shot vertically upwards in the air just to scare the thieves by a policeman. Initial velocity of the bullet is 30 m/s. After how much time after being shot, the bullet is going upward with 15 m/s speed? Resistance of air should be neglected.

A stone on Earth, where the acceleration due to gravity is g, is thrown vertically upward by an astronaut so that it returns to its starting point after 10.0 s. What is the speed with which the stone was thrown by the astronaut?

A football on Earth, where the acceleration due to gravity is g, is kicked vertically upward by player so that it returns to its starting point after 10.0 s. What is the maximum height reached by the football?

If a tennis ball is thrown vertically upward from a ground with an initial speed of 10.0 m/s, then what is the time taken by the ball to reach the ground?

If a juggler throws a bowling pin vertically upward to reach a maximum height of 10.00 m, then what is its time of flight?

If a body is projected vertically upward from a ground to reach a maximum height of 10.00 m, then what is its speed with which it is projected initially from the ground?

You throw a stone vertically upward from the edge of a cliff, whose height is 60.0 m. The stone reaches the starting point 10.00 s after it was thrown. Neglecting air resistance. What is the speed of the stone when it strikes the pond near the base of the cliff?

A small rock is thrown by you vertically upward with a speed of 10.0 m/s towards the ceiling, which is 4.0 m above the point where the small rock leaves your hand. How much is the time taken by the small rock to strike the ceiling?

You throw a cricket ball vertically upward with a speed of 10.0 m/s towards the roof top, which is 4.0 m above the point where the ball leaves your hand. What is the speed of the cricket ball just before it hits the roof top?

A ball is thrown vertically upward with a speed of 10.0 m/s from the top of a building of height 50.0-m. If air resistance is negligible, then in how much time the ball reaches the ground?

A stone is thrown vertically upward with a speed of 10.0 m/s from the top of the cliff of height 50.0-m. If air resistance is negligible, then with what speed the stone strikes the ground?

A 30-kg brick is released from a certain height on the earth and touches the surface of the ground in 0.217 s. But the brick touches the surface of the ground in 9.0 s when it is released from the same height on Mar's natural satellite Phobos. What will be the acceleration due to gravity on the surface of Phobos?

A stone is dropped from the top of a tower. The stone hits the ground in 3.80 s. Air resistance is neglected, so the stone is falling under the influence of gravity. What is the stone's speed as it touches the ground?

A ball is dropped from the top of a cliff. The ball hits the ground in 3.80 s. Air resistance is neglected, so the ball is in free fall under gravity. What is the height of the cliff?