Question

You and your friend throw balloons filled with water from the roof of a several story apartment house. You simply drop a balloon from rest. A second balloon is thrown downward by your friend 2.6 s later with an initial speed of 50.96 m/s. They hit the ground simultaneously. How high is the apartment house? The acceleration of gravity is 9.8 m/s 2 . Neglect air resistance.

Answer 1

Answer:

74.529 m

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.8 m/s²

For first ball

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=0\times t+\frac{1}{2}\times 9.8\times t^2\\\Rightarrow s=4.9t^2\ m$

For second ball

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=50.96\times (t-2.6)+\frac{1}{2}\times 9.8\times (t-2.6)^2\\\Rightarrow s=25.48t-99.372+4.9t^2$

As the displacement is equal

$25.48t-99.372+4.9t^2=4.9t^2\\\Rightarrow t=\frac{99.372}{25.48}\\\Rightarrow t=3.9\ s$

$s=4.9\times 3.9^2=74.529\ m$

So, height of the building is 74.529 m