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**

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