Vertical Motion and Free Fall Practice Problems

The operation of a winch is divided into three successive stages: acceleration period (a₁ = +0.50 m/s²), constant speed period (v = 2.5 m/s), and deceleration period (a₃ = - 0.50 m/s²). 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/s² 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/s². 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 velocity 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 CaCl₂ 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/s².

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/s². 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/s². 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?

A child drops a ball from the top of the building which reaches the ground after 5.30 s. Calculate the height of the building.

An object is released from the top of a tower and falls freely under the influence of gravity. How long does it take for the object to reach a speed of 45 km/h?

A stone is thrown vertically upward from the ground with an initial speed of 18 m/s. Calculate the maximum height it reaches above the ground.

High-jump athletes often clear the bar by leaping vertically. If a high jumper clears a bar at a height of 2.0 m, how much time does the athlete spend in the air during the jump?

A toy rocket is spotted ascending vertically past the edge of a cliff with a vertical speed of 10.0 m/s. If the rocket was launched from the base of the cliff, which is 30.0 m below the cliff's edge, determine the time between when it was launched to when it was seen passing the edge of the cliff.

A boy standing on a cliff 30.0 m above the ground observes a bird in the sky dropping a stone. The stone hits the ground 1.58 s after it passes the cliff. Determine the height from which the bird releases the stone. Assume the stone is initially at rest.

A ball falling from rest takes 0.64 seconds to pass a platform that is 4.0 meters tall. Determine the height above the top of the platform from which the ball fell.

In a safety assessment for amusement park rides, engineers drop test dummies from different heights to model various collision scenarios. Calculate the height from which a test dummy should be dropped to simulate a collision at 25 kmph.

A daredevil executes a high dive from a platform 30 meters above the water's surface. An inflatable cushion is positioned in the water to ensure a secure landing. The cushion undergoes a 3-meter expansion before gradually halting the daredevil's descent. Determine:

(i) The mean deceleration encountered by the daredevil as they were brought to a halt by the inflatable cushion.

(ii) If the objective is to enhance safety during the dive by reducing the deceleration, should the inflatable cushion's stiffness be increased or decreased?

A tennis ball is hit vertically from the ground and passes by a 3.00 m tall flagpole. The ball takes 0.20s to clear the entire height of the flagpole whose base starts 5.00 m above the ground. Calculate i) the speed of the ball after it got hit and ii) the height reached by the ball.

In a military exercise, bombs are being dropped from a 25.0 m high bridge. If it takes a regular soldier 0.50 seconds to react and protect themselves from the falling bomb, what's the lowest height at which they need to see the bomb coming to avoid getting hit successfully?

A stone is thrown vertically upwards which travels up to a height of 20.0 m with an acceleration of 1.2 m/s² and thereafter its acceleration is equal to acceleration due to gravity. Determine the maximum height attained by the stone.

As a hot air balloon rises vertically at a steady rate of 8.0 m/s, a sandbag is dropped from the balloon when it reaches an elevation of 300 m above the ground. Determine the time it takes for the sandbag to descend to the ground.

A watermelon falls from a tree branch 4.0 m above the ground. The watermelon weighs 8.0 kg. Calculate the speed of the watermelon just before it hits the ground.

At the exact same moment, two balls are thrown vertically upwards into the air. The second ball reaches a height that is 2.50 times higher than the first ball. Calculate what the initial speed of the second ball will be, given that the initial speed of the first ball is 5.00 m/s.

A circus acrobat performs a daring stunt by jumping off a high platform. Initially, the acrobat free-falls for 12.0 m. The acrobat reaches the safety net which provides a deceleration of -12.5 m/s² and finally, he lands on the ground with a speed of 5.00 m/s. Determine the height of the platform from which the acrobat jumped. Neglect air resistance.

Tom is able to fire his arrow vertically with a velocity that is 1.80 times greater than the velocity of Alex's arrow. Determine how much higher Tom's arrow will go up into the air compared to Alex's arrow when they are both fired vertically from the same starting point.

Model rockets are an effective way for students to learn about forces and how vehicles respond to external forces. Consider a model rocket (mass = 300g) whose motor yields 3.2 N of thrust. Neglecting air resistance, calculate the rocket's velocity when it reaches an altitude of 15 m.

A space shuttle is moving at 400 m/s in a region where the effect of gravitation is negligible. The shuttle accelerates at time t=0 s, by consuming all its fuel at a steady rate in 40 s. The exhaust gases are ejected at a constant speed of 1250 m/s. The empty shuttle mass is 1100 kg and the fuel mass is 400 kg. Find the shuttle's speed at i) t =20 s and at ii) t= 40 s.

An athlete tossed a ball vertically upward with a speed of v₁. A velocity sensor placed exactly 3.0 m above the point of release of the ball measures a speed of 8.0 m/s when the ball is at the same horizontal level as the sensor and moving upward. Calculate v₁.

A standard laboratory experiment consists of dropping charged particles through an opening into an electric field, where they will be suspended. A charged particle initially at the top of the apparatus (point O) falls for a distance OA of 0.80 m. Once the particle reaches point A, an instantaneous electric field is applied. As a result, the particle is stopped momentarily by the electric field in an 820 μs time interval. Calculate the magnitude of the acceleration encountered by the particle due to the electric field.

A construction worker accidentally drops a tool from the top of a building under construction. Assuming the tool falls freely from rest, determine the correct expression that represents the ratio of the increased distances traveled by the tool in each successive second of its descent.