Question

The height of a volleyball, h, in feet, is given by h = −16t^2 + 11t + 5.5, where t is the number of seconds after it has been hit by a player. The top of the net is 7.3 feet above the floor. Does the volleyball travel high enough to clear the top of the net? Please help me answer the steps attached below.

Answer 1

The volleyball travel high enough to clear the top of the net.

Explanation:

The height of a volleyball, h, in feet, is given by h = −16t² + 11t + 5.5, where t is the number of seconds after it has been hit by a player.

Now, for h = 7.3 feet, we can write

7.3 = - 16t² + 11t + 5.5

⇒ 16t² - 11y + 1.8 = 0

Using the quadratic formula we get,

`t = \frac{- (- 11) \pm \sqrt{(-11)^(2) - 4(16)(1.8)}}{2(16)}`

⇒
`t = (11 \pm 2.4)/(32)`

⇒ t = 0.27 or t = 0.42

Therefore, for the two real positive values of t the volleyball travel high enough to clear the top of the net. (Answer)