Question

A paper clip is dropped from the top of a 144‐ft tower, with an initial velocity of 16 ft/sec. Its position function is s(t) = −16t2 + 144. What is its velocity in ft/sec when it hits the ground?

-96
-64
-32
0

Answer 1

$\bf s(t)=-16t^2+144\implies \stackrel{velocity}{\cfrac{ds}{dt}}=-32t$

when does it hit the ground?  check the picture below.

$\bf 0=-16t^2+144\implies 16t^2=144\implies t^2=\cfrac{144}{16}\implies t^2=9 \\\\\\ t=\sqrt{9}\implies t=3$

at that moment, the velocity is -32(3).