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At time t=0,$ a ball is thrown downward at 24 feet per second from a height of 160 feet above the ground. The equation h = -16t^2 - 24t +160$ describes the height (in feet) of the ball. In how many seconds will the ball hit the ground? Express your answer as a decimal.

samus May 23, 2019

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$h(t) = -16t^2 -24t+160 = 8(-2t^2-3t+20)\\~\\ h(t) = 0 \Rightarrow (2t^2+3t-20)=0\\~\\ t \dfrac{-3\pm \sqrt{9+160}}{4} = \dfrac{-3\pm 13}{4} = \dfrac 5 2,-4\\~\\ \text{Clearly $\dfrac 5 2s = 2.5s$ is the solution we want}$

Rom May 23, 2019

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Rom · Answer 1 · 2019-05-23T08:22:19

$h(t) = -16t^2 -24t+160 = 8(-2t^2-3t+20)\\~\\ h(t) = 0 \Rightarrow (2t^2+3t-20)=0\\~\\ t \dfrac{-3\pm \sqrt{9+160}}{4} = \dfrac{-3\pm 13}{4} = \dfrac 5 2,-4\\~\\ \text{Clearly $\dfrac 5 2s = 2.5s$ is the solution we want}$

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