Question

Jason is serving in tennis. He hits the ball from a height of 2.5m and the path of the ball is given by y= -0.05x-0.005x², where the origin is the point where he hits the ball.

a)The net is 0.9m high and is 12m away. Does the ball pass over the net?
b)For the serve to be allowed it must land between the net and the service line, which is 18m away. Is the serve allowed?

Answer 1

Explanation:

a) To determine if the ball passes over the net, we need to find the height of the ball when it reaches x=12m (where the net is located).

y = -0.05x - 0.005x^2

y = -0.05(12) - 0.005(12)^2

y = -0.6 - 0.72

y = -1.32m

The ball reaches a height of -1.32m when it passes over the net, which is lower than the height of the net (0.9m). Therefore, the ball does pass over the net.

b) To determine if the serve is allowed, we need to find the horizontal distance where the ball lands and check if it is between the net and the service line (18m away from the origin).

We can find the distance the ball travels horizontally by finding the value of x when y = 0 (i.e., the height of the ball is 0 when it lands).

0 = -0.05x - 0.005x^2

0.005x^2 + 0.05x = 0

x(0.005x + 0.05) = 0

x = 0 (when the ball is hit) or x = -10 (when the ball lands)

The negative value of x indicates that the ball lands behind the server. Therefore, the serve is not allowed.