Answer
a. $2$ sec. $64$ ft/sec.
b. $12.31$ sec. $393.85$ ft.
Work Step by Step
a. Given the equation for the paper clip $s(t)=64t-16t^2$ ft, we have $v(t)=s'(t)=64-32t$ ft/sec and $a(t)=v'(t)=-32ft/s^2$. When the paper clip reaches its maximum, $v(t)=0$ and we get $t=2$sec. The initial velocity can be obtained as $v(0)=64$ ft/sec.
b. The equation on the moon changed to $s(t)=64t-2.6t^2$ ft. In this case, we have $v(t)=s'(t)=64-5.2t$ ft/sec and $a(t)=v'(t)=-5.2ft/s^2$. When the paper clip reaches its maximum, $v(t)=0$ and we get $t=64/5.2\approx12.31$ sec. The maximum height can be found as $s(12.31)=64(12.31)-2.6(12.31)^2\approx393.85$ ft.
