2. 1D Motion / Kinematics

Vertical Motion and Free Fall

Physics, Kinematics, Free Fall - Height Reached from Known Initial Velocity

You throw a glob of putty straight up toward the ceiling, which is 3.60 m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.50 m/s. (a) What is the speed of the putty just before it strikes the ceiling?

You throw a glob of putty straight up toward the ceiling, which is 3.60 m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.50 m/s. (b) How much time from when it leaves your hand does it take the putty to reach the ceiling?

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point 30.0 m below its starting point 5.00 s after it leaves the thrower’s hand. Ignore air resistance. (a) What is the initial speed of the egg?

A toy rocket starts on the ground at rest. Its engine burns for <math display="inline"><mrow><mn>3.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow></math> giving it a constant acceleration of <math display="inline"><msup><mrow><mn>4.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mi mathvariant="normal" class="MathML-Unit">m</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow></mrow><mn>2</mn></msup></math>. What is the maximum height achieved by the rocket?

A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0 s later. What was the rocket’s acceleration?

Free Fall: Concepts

A steel ball is dropped onto a thick piece of foam. The ball is released 2.5 meters above the foam. The foam compresses <math display="inline"><mrow><mn>3.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></math> as the ball comes to rest. What is the magnitude of the ball's acceleration as it comes to rest on the foam? Ignore air resistance.

Anderson Video - Free Fall and Gravity

Physics, Kinematics, Free Fall - Final Velocity at Bottom

Physics, Kinematics, Free Fall - Solving for Final Velocity, No.1

A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 1.90 s. You may ignore air resistance, so the brick is in free fall. (a) How tall, in meters, is the building?

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall. (b) What is the bearing’s impact velocity?

Physics, Kinematics, Free Fall - Solving for Final Velocity, No. 2

(a) v0y=37.5 m/s (b) vy=22.8 m/s

(a) v0y=16.7 m/s (b) vy=2 m/s

(a) v0y=2 m/s (b) vy=0 m/s

A student throws a set of keys vertically upward to her sorority sister who is in a window 14.00 m above. The second student catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00 m/s, releases a sandbag at an instant when the balloon is 40.0 m above the ground (Fig. E2.44). After the sandbag is released, it is in free fall. (d) What is the greatest height above the ground that the sandbag reaches? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/7b5db3469e2de19e-Untitled-2.png" alt="" /><img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/3f307ed1ba16eb26-1678190523846.jpg" style="width: 165px;">

(a) vy = 36.6 m/s downward; (b) t = 3.88 s

(a) vy = 11.0 m/s downward; (b) t = 3.88 s

(a) vy = 37.0 m/s downward; (b) t = 34.2 s

(a) vy = 36.6 m/s downward; (b) t = 6.49 s

A rock is thrown vertically upward with a speed of 27.0 m/s from the roof of a 31.0-m-tall building. The rock doesn't hit the building on its way back down and lands in the street below. (a) What is the speed of the rock just before it hits the street? (b) How much time elapses from when the rock is thrown until it hits the street?

(a) If a flea can jump straight up to a height of 0.440 m, what is its initial speed as it leaves the ground?

A tennis ball on Mars, where the acceleration due to gravity is 0.379g and air resistance is negligible, is hit directly upward and returns to the same level 8.5 s later. (a) How high above its original point did the ball go?

A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30 m/s² for 30 s, then runs out of fuel. Ignore any air resistance effects.

a. What is the rocket’s maximum altitude?

A 7500-kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.25 m/s2 and feels no appreciable air resistance. When it has reached a height of 525 m, its engines suddenly fail; the only force acting on it is now gravity. (a) What is the maximum height this rocket will reach above the launch pad?

A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00 m/s, releases a sandbag at an instant when the balloon is 40.0 m above the ground (Fig. E2.44). After the sandbag is released, it is in free fall. (a) Compute the position and velocity of the sandbag at 0.250 s and 1.00 s after its release. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/e636f157ffc22a1f-Untitled-1.png" alt="" /><img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/2351733b999f235b-1678190452532.jpg" style="width: 182px;">

A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (d) When is the velocity of the boulder zero?

A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (a) At what time after being ejected is the boulder moving at 20.0 m/s upward?

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point 30.0 m below its starting point 5.00 s after it leaves the thrower’s hand. Ignore air resistance. (c) What is the magnitude of its velocity at the highest point?

A small rocket burns 0.0500 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1600 m/s. (a) What is the thrust of the rocket?

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point 30.0 m below its starting point 5.00 s after it leaves the thrower’s hand. Ignore air resistance. (b) How high does it rise above its starting point?

A hotel elevator ascends 200 m with a maximum speed of 5.0 m/s. Its acceleration and deceleration both have a magnitude of 1.0 m/s².

b. How long does it take to make the complete trip from bottom to top?

(b) If a flea can jump straight up to a height of 0.440 m, How long is it in the air?

A 7500-kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.25 m/s2 and feels no appreciable air resistance. When it has reached a height of 525 m, its engines suddenly fail; the only force acting on it is now gravity. (b) How much time will elapse after engine failure before the rocket comes crashing down to the launch pad, and how fast will it be moving just before it crashes?

A lunar lander is making its descent to Moon Base I (Fig. E2.40). The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is 5.0 m above the surface and has a downward speed of 0.8 m/s.With the engine off, the lander is in free fall. What is the speed of the lander just before it touches the surface? The acceleration due to gravity on the moon is 1.6 m/s <img src="https://lightcat-files.s3.amazonaws.com/problem_images/34120ff9426d7bb8-Untitled-5.png" alt="" /><img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/8a2194b74e78eed8-1678178522787.jpg" style="width: 174px;">

A small rocket burns 0.0500 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1600 m/s. (b) Would the rocket operate in outer space where there is no atmosphere? If so, how would you steer it? Could you brake it?

A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 1.90 s. You may ignore air resistance, so the brick is in free fall. (b) What is the magnitude of the brick’s velocity just before it reaches the ground?

A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (e) What are the magnitude and direction of the acceleration while the boulder is (i) moving upward? (ii) Moving downward? (iii) At the highest point?

A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (b) At what time is it moving at 20.0 m/s downward?

Physics, Kinematics, Free Fall -  Solving for Time to Fall from Known Height

A small rock is thrown vertically upward with a speed of 22.0 m/s from the edge of the roof of a 30.0-m-tall building. The rock doesn’t hit the building on its way back down and lands on the street below. Ignore air resistance. (a) What is the speed of the rock just before it hits the street?

A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (c) When is the displacement of the boulder from its initial position zero?

When jumping, a flea accelerates at an astounding 1000 m/s^2, but over only the very short distance of 0.50 mm. If a flea jumps straight up, and if air resistance is neglected (a rather poor approximation in this situation), how high does the flea go?

As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 35 m/s. How fast is the watermelon going when it passes Superman?

A small rock is thrown vertically upward with a speed of 22.0 m/s from the edge of the roof of a 30.0-m-tall building. The rock doesn’t hit the building on its way back down and lands on the street below. Ignore air resistance. (b) How much time elapses from when the rock is thrown until it hits the street?

A 15-kg rock is dropped from rest on the earth and reaches the ground in 1.75 s. When it is dropped from the same height on Saturn’s satellite Enceladus, the rock reaches the ground in 18.6 s. What is the acceleration due to gravity on Enceladus?

A lead ball is dropped into a lake from a diving board 5.0 m above the water. After entering the water, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the water. The ball reaches the bottom 3.0 s after it is released. How deep is the lake?

A rock is tossed straight up from ground level with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep. (a) What is the rock’s speed as it hits the bottom of the hole?

A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s. How much time elapses until the bowling pin returns to the juggler’s hand?

A steel ball is dropped onto a thick piece of foam. The ball is released 2.0 meters above the foam. The foam compresses <math display="inline"><mrow><mn>3.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></math> as the ball comes to rest. How fast is the ball moving when it first hits the foam? Ignore air resistance.

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall. (a) If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?

A 1000 kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16 s, then the motor stops. The rocket altitude 20 s after launch is 5100 m. You can ignore any effects of air resistance. What was the rocket’s acceleration during the first 16 s?

A tennis ball on Mars, where the acceleration due to gravity is 0.379g and air resistance is negligible, is hit directly upward and returns to the same level 8.5 s later. (b) How fast was it moving just after it was hit?

Free Fall: Initial Velocity Effects

Anderson Video - Time for Dropped Object to Hit Ground

How Long Are You in the Air During a Dunk? | Physics with Professor Matt Anderson | M2-08

You throw a small rock straight up from the edge of a highway bridge that crosses a river. The rock passes you on its way down, 6.00 s after it was thrown. What is the speed of the rock just before it reaches the water 28.0 m below the point where the rock left your hand? Ignore air resistance.

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point 30.0 m below its starting point 5.00 s after it leaves the thrower’s hand. Ignore air resistance. (d) What are the magnitude and direction of its acceleration at the highest point?

Vertical Motion & Free Fall

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