Answer
$-4 \sqrt {245}$ or, $-62.61$
Work Step by Step
When the objetc hits the ground at that moment , then $s(a)=0 \implies -4.9a^2+200=0$
After solving we get $a=\sqrt{\dfrac{200}{4.9}}$ ...(1)
Now, $v(a)=\lim\limits_{t \to a}\dfrac{s(t)-s(a)}{t-a}=\lim\limits_{t \to a}\dfrac{-4.9t^2+200+4.9a^2-200}{t-a}$
or, $\lim\limits_{t \to a}\dfrac{-4.9t^2+200+4.9a^2-200}{t-a}=-4.9\lim\limits_{t \to a}\dfrac{(t-a)(t+a)}{t-a}=-9.8a$
Fro equation (1), we have $v(a)=-9.8a=(-9.8) (\sqrt{\dfrac{200}{4.9}})=-4 \sqrt {245}$ or, $-62.61$
