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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?

 Dec 31, 2020
edited by Guest  Dec 31, 2020
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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.  :)))))

=^._.^=

 Dec 31, 2020

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