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# The equation $y = -16t^2 - 60t + 54$ describes the height (in feet) of a ball thrown downward at 60 feet per second from a height of 54 feet

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The equation $y = -16t^2 - 60t + 54$ describes the height (in feet) of a ball thrown downward at 60 feet per second from a height of 54 feet from the ground, where $t$ represents time, measured in seconds. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest hundredth.

Mar 26, 2021

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Setting $y$ to zero, we get the quadratic $-16t^2 - 60t + 54 = 0.$Dividing both sides by $-2,$ we get $8t^2 + 30t - 27 = 0.$This quadratic factors as $(4t - 3)(2t + 9) = 0.$ As $t$ must be positive, we can see that $t = \frac{3}{4} = \boxed{0.75}.$

Mar 26, 2021
edited by WillBillDillPickle  Mar 26, 2021
edited by WillBillDillPickle  Mar 26, 2021

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By the quadratic formula, the ball hits the ground in 0.65 seconds.

Mar 26, 2021
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Its actully 0.75.

Mar 26, 2021
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Setting $y$ to zero, we get the quadratic $-16t^2 - 60t + 54 = 0.$Dividing both sides by $-2,$ we get $8t^2 + 30t - 27 = 0.$This quadratic factors as $(4t - 3)(2t + 9) = 0.$ As $t$ must be positive, we can see that $t = \frac{3}{4} = \boxed{0.75}.$