Question

Patricia serves the volleyball to Amy with an upward velocity of 17.5ft/s. The ball is 5 feet above the ground when she strikes it. How long does Amy have to react, before the volleyball hits the ground? Round your answer to two decimal places.

Answer 1

t = 1.33 sec

Solution:

Given data:

Velocity $(v_0)$ = 17.5 ft/s

Height $(h_0)$ = 5 ft

The height can be modeled by a quadratic equation

$h(t)=-16t^2+v_0t+h_0$

where h is the height and t is the time

$h(t)=-16t^2+17.5t+5$

$-16t^2+17.5t+5=0$

a = –16, b = 17.5, c = 5

It looks like a quadratic equation. we can solve it by quadratic formula,

$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\Rightarrow t=\frac{-17.5 \pm \sqrt{(-17.5)^{2}-4\times (-16)(5)}}{2 (-16)}$

$\Rightarrow t= \frac{-17.5 \pm \sqrt{306.25+ 320}}{-32}$

$\Rightarrow t= \frac{-17.5 \pm 25.025}{-32}$

$\Rightarrow t= \frac{-17.5 - 25.025}{-32}, \ t= \frac{-17.5 + 25.025}{-32}$

$\Rightarrow t= 1.33, \ t= -0.24$

Time cannot be in negative. So neglect t = –0.235.

t = 1.33 sec

Hence Amy have to react  1.33 sec before the volleyball hits the ground.