Question

Marsha serves the Volleyball to Rhonda with an upward velocity of 14.5 ft./s. The bar is 4 feet above the ground when she strikes it. How long does Rhonda have to react, before the Volleyball hits the ground? Round your answer to two decimal places.

Answer 1

The taken by Rhonda to react before volleyball hits ground is 2.39 seconds

Explanation:

Given as :

The upward velocity of the volleyball = 14.5 ft/s

The height of the ball above ground = 4 feet

Consider value of acceleration due to gravity = 9.8 m/s

Let the time for Rhonda to react before ball hits ground = t sec

Now,

S = u t +
`(1)/(2)` a t²

where s = height

u = initial velocity , a = acceleration due to gravity , t = time in sec

So, 4 = 14.5× t +
`(1)/(2)` × 9.8 × t²

or, 4 = 14.5 t + 4.9 t²

or, 4.9 t² + 14 .5 t - 4 = 0

Now, solve for t

t =
`\frac{-b\pm \sqrt{b^(2)-4* a* c}}{2* a}`

or, t =
`\frac{-14.5\pm \sqrt{14.5^(2)-4* 4.9* (4)}}{2* 4.9}`

Or, t =
`(-14.5\pm √(80.5025))/(9.8)`

Or, t = - 2.39 , - 2.76

Hence The taken by Rhonda to react before volleyball hits ground is 2.39 seconds . Answer