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...

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