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?
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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. :)))))
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