# How do you find the height of the roof in the following case: A tennis player, standing at the edge of her building's roof throws her tennis ball straight up with an initial speed of of 6.00 m/s. The ball then reaches the ground in 3.35 s. We have to use the concepts of motion here. The tennis player throws the ball straight up with an initial speed of 6 m/s.

There is an acceleration acting on the ball due to the gravitational force of attraction which is equal to 9.8 m/s^2 acting downwards.

Let the height of the roof be H. The ball rises up and due to the acceleration its speed reduces, until it reaches 0 m/s. Then the ball starts to fall down.

We first find the time taken to reach the highest point. We have the relation t = ( v - u) / a = (6/9.8)

The highest point reached by the ball is u*t + (1/2)*a*t^2 above the roof.

=> 6*(6/9.8) - (1/2)(9.8)((6/ 9.8)^2

From this point the ball falls towards the ground. The time taken by it to do so is 3.35 - (6/9.8)

So we have 6*(6/9.8) - (1/2)(9.8)((6/ 9.8)^2 + H = 0 + (1/2)*9.8*(3.35 - (6/9.8))^2

We solve 6*(6/9.8) - (1/2)(9.8)((6/ 9.8)^2 + H = (1/2)*9.8*(3.35 - (6/9.8))^2 for H.

6*(6/9.8) - (1/2)(9.8)((6/ 9.8)^2 + H = (1/2)*9.8*(3.35 - (6/9.8))^2

=> H = (1/2)*9.8*(3.35 - (6/9.8))^2 - 6*(6/9.8) + (1/2)(9.8)((6/ 9.8)^2

=> H = 34.89 m

The height of the roof is 34.89 m

Approved by eNotes Editorial Team

Posted on 