How far above the court is the tennis ball when it leaves the racket?

Question

A tennis ball is struck and departs from the racket horizontally with a speed of 27.8 m/s. The ball hits the court at a horizontal distance of 19.4 m from the racket. How far above the court is the tennis ball when it leaves the racket?

Answer 1

This is a parabolic motion question. From the horizontal speed and the distance traveled we can find how long the ball was in the air: t = x /v_h 

Then the vertical part of the problem uses the equation for parabolic motion: 

y_f = y_i + v_ot - 1/2 g t²

Since the ball was struck horizontally, v_o = 0. We want the height the ball was above the ground: y_i - y_f. Writing the question this way lets us not care where we draw y = 0. If you like, we can choose a y=0 point..a convenient place would be to have ground level be y = y_f = 0. 

Our answer is: y_i - y_f = 1/2 g t²