Question

1. Physics and astronomy student club has a recently established tradition of pumpkin drop, from the top of Wick Science Building to the "moat" below street level. Although the "experimental data" have not been made public, there have been rumors of the drop took 2.07 seconds, i.e. falling from rest with negligible air drag. Based on the rumor, how tall is the building from the "moat" to the roof?

Ignore air drag or any rotation of pumpkins.

Hint: You may assume final position to be zero.

2. You accidentally knocked over your coffee mug you precariously set at the edge of your table while video chatting with a friend, causing it to fall from rest to the ground. You tried to catch it but failed. You claimed to your friend that the mug only took 0.15 seconds to fall, thus making it impossible for you to catch. How tall would your table be if your claim were true?

Ignore air drag or any rotation of your mug.

Hint: You may assume final position to be zero.

3. A diver jumps off the diving board at 1.6 m/s. Assume the diving board is 2.5 m above the water surface in the pool and the diver has a tiny forward velocity so she could clear the board in her way down and hit the water feet first, how long will it take her to strike the water surface?

Ignore air drag.

Hint: You can set the final position to be zero.

4. You are standing on your balcony in an apartment building. You tossed a coin straight upwards at 14 m/s. Assume the coin leaves your hand at 14 m above ground, how long will it take to strike the ground?

Ignore air drag.

Hint: You can set the final position to be zero

Answer

5. In a medieval castle siege reenactment, a castle defender threw down a "stone" (made of soft materials) with all his might, achieving an initial speed of 11 m/s downward. The castle was 7.5 m tall. How long will the attacker have before the "stone" hit the ground?

You can assume the final position to be zero. The "stone" has negligible amount of air drag.

Hint: the "stone" has a downward initial velocity.

6. A careless painter dropped a brush (with paint!) from a scaffold outside a building he's supposed to paint. You were just recording a selfie video across the street and caught the falling brush in your video. You used your physics skills to figure out the paint brush was falling at 4.0 m/s when it was just passing the top of a window that you estimated at 7.0 m above the ground. How long did it take the brush to fall from that height to the ground and make a colorful splash?

You can assume the final position to be zero. The paint brush has negligible amount of air drag.

Hint: the paint brush has a downward initial velocity at the height you estimated.

Answer 1

Multiple questions posted, so answering only the first question.

1. Under uniform acceleration, s=ut+1/2 at^2, where s is displacement, u is initial velocity , a is acceleration and t is time.

Let the downward direction be positive.

Final position = 0 m, initial position = - h, where h is the required height.

So, s=final position-initial position = 0-(-h) = h.

Also, for the given problem, u = 0 m/s(the object was dropped from rest), t = 2.07 s, a = 9.8 m/s2

So, h= 0 *2.07+1/2*9.8*2.07*2.07 = 21 m.

So, required height = 21 m.