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

Answer:

3.29 s

Step-by-step 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:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Using the quadratic formula

$t=\frac{-5\pm\sqrt{25+960}}{8}$

$t=\frac{-5\pm\sqrt{985}}{8}$

$t=\frac{-5+31.28}{8}=3.29 s$

$t=\frac{-5-31.38}{8}=-4.5$

Time cannot be negative .Therefore,

t=3.29 s