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...
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.
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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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