Question

sharon serves the volleyball to rhonda with an upward velocity of 18.5 ft/s. The ball is 4.5 feet above the ground when she strikes it . How long does rhonda have to react before the volleyball hits the ground

Answer 1

we can use height formula

$h(t)=-\frac{1}{2} g t^2+vt+h(0)$

where

h(t) is the height after t seconds

v is velocity

h(0) is initial height

g is acceleration due to gravity

we know that

g=32 ft/s^2

we have

v=18.5ft/s

h(0)=4.5ft

so, we can plug these values

and we get

$h(t)=-\frac{1}{2}*32 t^2+18.5t+4.5$

$h(t)=-16 t^2+18.5t+4.5$

now, we have to find time when object will hit the ground

and we know that object will hit the ground when height becomes 0

so, we can set h(t)=0

and then we can solve for t

$0=-16 t^2+18.5t+4.5$

we can use pythagoras theorem

$t=\frac{-185-\sqrt{185^2-4\left(-160\right)45}}{2\left(-160\right)}=\frac{37+\sqrt{2521}}{64}$

$t=1.36265sec$..............Answer