How tall is the building?

Question

A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below.If the balloon is traveling at 32.1 m/s when it strikes a person's head(1.5 m above the ground),neglect air resistance.

Answer 1

Use conservation of energy (m)gh=1/2(m) v^2

Answer 2

This is Newtons's equations of motion.

Firstly, we need the time of the fall, therefore-:

v = u + at

v = final velocity
u = initial velocity
a = acceleration (in this case gravity)
t = time in seconds
(I am also assuming the balloon is falling from rest and not thrown with velocity)

thus, 32.1 = 0 + 9.8 t

32.1 / 9.8 = t = 3.2755 seconds

Now, use another equation of motion-:

s = ut + 1/2 a t^2
s = total distance
ut = initial velocity x time
a = acceleration due to gravity
t = time in seconds

s = 0 + 1/2 x 9.8 x 3.2755^2
s= 52.57 metres

Now add on the additional 1.5 m

Therefore-: 52.57 + 1.5 = 54.07 metres is the height of the building.