You are on the roof of a tall building. Your TA (who is 1.8m tall) is walking by

Question

You are on the roof of a tall building. Your TA (who is 1.8m tall) is walking by, and you drop (from rest at the level of the roof) a water balloon on him. It takes 2s for the balloon to go from the roof of the building to your TA’s head. (a)[6 pts] How tall is the building? (b)[5 pts] What was the velocity of the balloon when it hit your TA? (c)[8 pts] If instead of dropping the balloon from rest, you threw it down (speed 10 m/s straight down as it passes the roof level), how fast would it be traveling when it hits your TA and how long would it take? (d)[5 pts] If the building was twice as tall, how long will it take an object dropped from rest (at roof level) to hit the ground?

Explanation / Answer

h = height of building

d = displacement of balloon = h - 1.8

t = time = 2 s

a = acceleration = - 9.8 m/s2

Vo = initial velocity = 0 m/s

using the equation

d = Vo t + (0.5) a t2

h - 1.8 = 0 (2) + (0.5) (9.8) (2)2

h = 21.4 m

b)

Vf = Vi + a t = 0 + (9.8) (2) = 19.6 m/s

c)

using the equation

d = Vo t + (0.5) a t2

21.4 - 1.8 = 10 t + (0.5) (9.8) t2

t = 1.225 sec

Vf = Vi + a t = 10 + (9.8) (1.225) = 22.01 m/s

d)

using the equation

h = Vo t + (0.5) a t2

2 x 21.4 = 0 t + (0.5) (9.8) t2

t = 2.96 sec

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