What minimum speed is required for the ball to clear the 0.90 m net about 15.4 m from the serve if the ball is “launched” from a height of 2.6 m.

Question

Tennis players aim to hit the ball horizontally during their serve. What minimum speed is required for the ball to clear the 0.90 m net about 15.4 m from the serve if the ball is “launched” from a height of 2.6 m. 

Answer 1

Kristyn B.,

Were asked to find the speed in the x (horizontal) direction which can be acquired from x = v_xt or v_x = x/t. We know x (15.4 m) but we need to find t. We can find how long it takes for gravity to force the ball down from the initial height (tennis racket) to the final height (top of net) from y = y_o + v_ot + 1/2 at². We'll choose y to be positive up. The initial height y_o = 2.6 m, final height y = 0.90 m, the initial velocity in the y direction is zero v_o = 0, and a = -g (since y is positive up, gravity is downward and negative, -g = -9.8 m/s²).

We have:

0.90m = 2.6 m - 4.9 m/s² * t²

4.9 m/s² * t² = 1.7 m

t = ± [ 1.7 m / 4.9 m/s² ]^1/2

t = ± 0.6 s (choose + s)

The velocity in the x direction:

v_x = 15.4 m / 0.6 s = 26 m/s minimum horizontal speed.

Have fun! I hope this helps, Joe.