# A bullet is fired upward from ground level. Its height above the ground (in feet) at time t seconds is given by H = -16t^2 + 1000t. How many seconds does it take the bullet to return to ground level?

Apr 20, 2018

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#### Explanation:

You are looking for the moment when H will be 0 again. That is

$0 = - 16 {t}^{2} + 1000 t = t \left(- 16 t + 1000\right)$

this product will be zero if $t \mathmr{and} \left(- 16 t + 1000\right)$ are zero

$t = 0$ is the initial state (when gun is fired)

$- 16 t + 1000 = 0$ give $- t = - \frac{1000}{16} = - 62.5$. Thus $t = 62.5$ seconds