Question

use the position function s(t)=-16t^2 + 1000 which gives the height (in feet) of an object that has fallen for t seconds from a height of 1000 feet. the velocity at time t=a seconds is given by
lim t->a [s(a)-s(t)]/a-t

1. if a contruction worker drops a wrench from a height of 1000 feet, how fast will the wrench be falling after 5 seconds?
2. if a contruction worker drops a wrench from a height of 1000 feet, when will the wrench hit the ground? at what velocity will the wrench impact the ground?

Answer 1

\[v(t) = s'(t) = -32t\]
1) v(5) = -32(5) = -160
2)
Find when the height is zero:\[-16t^2 + 1000 = 0\]\[t = \frac{5}{2}\sqrt{10}\]\[v\left(\frac{5}{2}\sqrt{10}\right) = -32 \left(\frac{5}{2}\sqrt{10}\right) = 80\sqrt{10}\]