Question

1.

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.

2.

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.

3.

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 1

Multiple questions posted, so answering only the first question:

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

For the given problem, s= 7 m, u = 4m/s, a=10 m/s2(gravitational acceleration on earth)

So, 7 = 4t+1/2*10*t^2

=>5t^2+4t-7=0

=>t={-4+[4*4+4*5*7]^0.5}/(2*5) (using quadratic formula and taking only the positive root as time cannot be negative)

= 0.85 seconds.

So, required time=0.85 seconds.