Question

A volleyball player serves the ball and makes contact 6 feet above the ground with an initial vertical velocity of 20 ft./s how long will it be before the ball hits the ground

Answer 1

1.5 seconds

Explanation:

You want to know when a ball launched from a height of 6 ft with a vertical velocity of 20 ft/s will hit the ground.

Ballistic motion

The equation for the height of the ball is ...

h(t) = -16t² +v0·t +h0

where v0 and h0 are the initial vertical velocity and height, respectively.

Application

For the given parameters, the equation is ...

h(t) = -16t² +20t +6

The solution to h(t) = 0 can be found using the quadratic formula:

0 = -16t² +20t +6 . . . . . . . a=-16, b=20, c=6

`t=(-b\pm√(b^2-4ac))/(2a)=(-20\pm√(20^2-4(-16)(6)))/(2(-16))\\\\\\t=(20\pm√(784))/(32)=(20\pm28)/(32)=\{-0.25,1.5\}`

The ball will hit the ground after 1.5 seconds.

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