posted by Gina on .
You serve a tennis ball from a height of 1.8 m above the ground. The ball leaves your racket with a speed of 19.4 m/s at an angle of 7.28° above the horizontal. The horizontal distance from the court's baseline to the net is 11.83 m, and the net is 1.07 m high. Neglect spin imparted on the ball as well as air resistance effects. Does the ball clear the net?
If yes, by how much? If not, by how much did it miss?
Write the equations for ball height Z and horizontal location X vs time. Assume the ball is served perpendicular to the net, "down the middle" (Y=constant), not to a side line.
X = 19.4 cos 7.28 t = 19.24 t
When the ball reaches the net, X = 11.83 m, so t = 0.6149 s
Y = 1.80 + 19.4 sin 7.28 t - (9.80/2)t^2
= 1.80 + 2.468 t - 4.90 t^2
Solve for the Y height when t = 0.6149 s when the ball reaches the net), and compare it to the height of the net.
I get Y to exceed the net height when it reaches the net.
The equation for Y should have been for the ball height, Z.