A tennis court is 78 feet long with a net stretched across the center. The distance from the net to the back is 39 feet long, and the net itself is 3 feet long.
Assuming Carina hits the ball as hard as she can, from what height must she hit the ball to have the return shot just clear the fence. Decide whether or not it is reasonable for Carina the real this height if she is 5'7" and using a traditional racket of 27"
I wil assume 'clear the fence' means 'clear the net' AND she is hitting the ball PERPINDICULAR to the net from 39 feet (468 inches) and not diagonal across the court..... I will also assume she hits the ball from a height equal to her height PLUS the racquet length of 27 " = 94 inches (sorry for all of the assumptions. but this info is not included in the Question) I will also have to assume she hits the ball horizontally with no VERTICAL velocity....Also have to assume the net is 36 inches HIGH (not long)
Ball position in the horizontal distance is equal to
x = xo + vot + 1/2 a/t^2 (1)
Let's do the 'y' component first
36 inches = 94 inches + (0)t + 1/2 a t^2 t = 1.898 secs (vo in the VERTICAL direction is zero since she hits the ball horizontally)
Now for the 'x' (horizontal ) calcs:
39 ft (12 in/ft) = 0 + vot + 1/2 a t^2 For this a = 0 (negleting air friction)
39(12) = vo t and t = 1.898 sec so vo = 246.57 in/sec = 20.54 f/s