Answer
$1.24sec$
Work Step by Step
Step 1. Given $\frac{d^2s}{dt^2}=-5.2ft/s^2$, we can get $\frac{ds}{dt}=\int(-5.2)dt=-5.2t+C$ and $s=\int(-5.2t+C)dt=-2.6t^2+Ct+D$, where $C$ and $D$ are constants.
Step 2. At $t=0, \frac{ds}{dt}=0$, we have $-5.2(0)+C=0$ and $C=0$
Step 3. At $t=0, s=4$, we have $-2.6(0)^2+D=4$ and $D=4$. Thus $s=\int(-5.2t+C)dt=-2.6t^2+4$
Step 4. Let $s(t)=0$, we have $-2.6t^2+4=0$ which gives $t=\sqrt {\frac{20}{13}}\approx1.24sec$
Step 5. It takes the hammer and feather about $1.24$ seconds to fall 4 ft on the moon.
