Question

A ball is thrown downward from the top of a 240​-foot building with an initial velocity of 20 feet per second. The height of the ball h in feet after t seconds is given by the equation h= -16t^2 - 20t + 240. How long after the ball is thrown will it strike the​ ground?

Answer 1

3.29 s

Explanation:

We are given that

Height of building=240

Initial velocity=20ft/s

The height of the ball after t seconds is given by

`h(t)=-16t^2-20t+240`

When the ball strike the ground then

h(t)=0

`-16t^2-20t+240=0`

`4t^2+5t-60=0`

Quadratic formula:

`x=(-b\pm√(b^2-4ac))/(2a)`

Using the quadratic formula

`t=(-5\pm√(25+960))/(8)`

`t=(-5\pm√(985))/(8)`

`t=(-5+31.28)/(8)=3.29 s`

`t=(-5-31.38)/(8)=-4.5`

Time cannot be negative .Therefore,

t=3.29 s