Question

The equation $y = -16t^2 + 28t + 144$ describes the height $y$ (in feet) at time $t$ (in seconds) of a ball tossed up in the air at $28$ feet per second from a height of $144$ feet from the ground. In how many seconds will the ball hit the ground?

Answer 1

4 seconds

Explanation:

Given the equation y = -16t² +28t +144 describes a ball's height as a function of time in seconds, you want to know when the ball will hit the ground.

Zero

The ball will hit the ground when the value of y is zero.

0 = -16t² +28t +144

t² -7/4t -9 = 0 . . . . . divide by 16

t² -7/4t +(7/8)² = 9 +(7/8)² . . . . . complete the square

t = 7/8 +√(9 49/64) = 7/8 +3 1/8 = 4 . . . . take the square root, add 7/8

The ball will hit the ground after 4 seconds.