The equation y = -16t^2 + 28t + 144 describes the height (in feet) 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?

Guest Dec 31, 2020

edited by
Guest
Dec 31, 2020

#1**0 **

Hello Guest!

0 = -16t^2 + 28t + 144 # The ball hits the ground when the height is 0 feet so we set y as 0.

0 = -4(4t^2 - 7t - 36) # Factor -4 from both sides

0 = -4(4t + 9)(t - 4) # Factor the quadratic

In order for the answer to be 0, we need 4t + 9 = 0 or t - 4 = 0.

4t + 9 = 0 # Case #1

4t = -9 # Subtract 9 from both sides

t = -9/4 # Divide 4 from both sides

t - 4 = 0 Case #2

t = 4 # Add 4 to both sides

t = −9/4 or t = 4

However, there is no such thing as negative seconds in this problem, so the ball hits the ground at 4 seconds.

I hope this helped. :)))))

=^._.^=

catmg Dec 31, 2020