Question

Table tennis 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?

Answer 1

Check the picture below.

the ball hits the table, when it hits "the ground" or goes all the way back down, at that point, the height of the ball is 0, thus h = 0.

$\bf 0=-4.9t(t-0.42)\implies t= \begin{cases} 0=-4.9t\\ 0=t\\ ------\\ 0=t-0.42\\ \boxed{0.42=t} \end{cases}$