# Question #9a724

Feb 6, 2018

$3.5 s$

#### Explanation:

graph{-16x^2+54x+7 [-5, 5, -5, 5]}

when the ball hits the ground, its height is $0$.

$h \left(t\right) = 0$

this means that $- 16 {t}^{2} + 54 t + 7 = 0$.

$\left(8 t + 1\right) \left(2 t - 7\right) = 16 t - 56 t + 2 t - 7 = 16 t - 54 t - 7$

$- \left(8 t + 1\right) \left(2 t - 7\right) = - 16 t + 54 t + 7$

factorising gives $- \left(8 t + 1\right) \left(2 t - 7\right) = 0$.

$0 = - 0$

$\left(8 t + 1\right) \left(2 t - 7\right) = 0$.

$8 t = - 1$ or $2 t = 7$

$t = - \frac{1}{8}$ or $t = \frac{7}{2}$

note that the answer asks for the height after $t$ seconds. this means that only the positive solution of $t$ applies.

here, this is $\frac{7}{2}$

$\frac{7}{2} = 3.5$

$3.5$ seconds after being thrown up from $7$ feet above ground, the ball will reach the ground again (assuming that the ground is level).