Answer
$20$ seconds
Work Step by Step
$$a=-32$$
$$\frac{dv}{dt}=-32$$
$$\int \frac{dv}{dt} dt =\int-32 dt$$
$$v(t) =-32t+C$$
Find $C$ using $v(0)=0$ so:
$$v(0) =-32\cdot 0+C=0 \to C=0 $$
so:
$$v(t) =-32t$$
$$\frac{ds}{dt}=-32t$$
$$\int \frac{ds}{dt} dt=\int-32t dt$$
$$s(t)=\frac{-32t^{2}}{2}+s_{0}$$
Find $s_{0}$ using $s(0)=6400$ so:
$$s(0)=\frac{-32(0)^{2}}{2}+s_{0}=6400 \to s_{0}=6400 $$
Therefore:
$$s(t)=\frac{-32t^{2}}{2}+6400$$
The object will hit the ground when $s(t)=0$ so:
$$0=\frac{-32t^{2}}{2}+6400$$
$$\frac{32t^{2}}{2}=6400$$
$$t=-20~~\text{or}~~t=20$$
Since the time is always positive then:
$$t=20$$
