The path of a table tennis ball after being hit and hitting the surface of the table can be modeled by the function h = - 4.9t (t-0.42) where h is the height in meters above the table and t is the time in seconds. How long does it take the ball to hit the table? What is the ball's maximum height?

The height (m) at time t (s) is

h (t) = - 4.9t (t - 0.42) = - 4.9t² + 2.058t

When the ball hits the surface of the table, h = 0.

Therefore

-4.9t (t - 0.42) = 0

t = 0, or t = 0.42 s

The interval between the two times is 0.42 s.

At maximum height, the velocity, v, is zero.

Therefore

v (t) = h' (t) = - 9.8t + 2.058 = 0

t = 0.21 s

The maximum height is

-4.9 * (0.21) ² + 2.058 (0.21) = 0.216 m

Answers:

(a) It takes 0.42 s to hit the table.

(b) The maximum height is 0.216 m