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

74.529 m

Step-by-step 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+(1)/(2)at^2\\\Rightarrow s=0* t+(1)/(2)* 9.8* t^2\\\Rightarrow s=4.9t^2\ m`

For second ball

`s=ut+(1)/(2)at^2\\\Rightarrow s=50.96* (t-2.6)+(1)/(2)* 9.8* (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=(99.372)/(25.48)\\\Rightarrow t=3.9\ s`

`s=4.9* 3.9^2=74.529\ m`

So, height of the building is 74.529 m