Physics Question Help?

Question

You and your friend throw balloons filled with
water from the roof of a several story apart-
ment house. You simply drop a balloon from
rest. A second balloon is thrown downward
by your friend 2.3 s later with an initial speed
of 45.08 m/s. They hit the ground simultane-
ously.
The acceleration of gravity is 9.8 m/s2 : You
can neglect air resistance.
How high is the apartment house? Answer in m

Answer 1

For balloon you drop

y(t)=h-.5*9.81*t^2

For your friend

y(t)=h-45.08*(t-2.3)-.5*9.81*(t-2.3)^2

solve for h when y(t)=0

h=9.81*t^2/2

0=9.81*t^2/2-45.08*t+2.3*45.08
-.5*9.81*(t^2-4.6*t+2.3^2)

t=77.737/22.517

t=3.4523

h=58.46 m

BTW: 45.08 m/s is about 100 mph. Not so hard to achieve when throwing straight down.
j

Answer 2

45 m/s? your friend has a hell of an arm......man.