Assume that air resistance is negligible, which implies that the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ is a reasonable model. A rock is dropped from the top of a 180-foot cliff that overlooks the ocean. How long will it take for the rock to hit the water? Round to the nearest hundredth of a second.
A)7.30 seconds
B)3.35 seconds
C)5.99 seconds
D)4.67 seconds
E)11.25 seconds

Question

Quizplus · Accepted Answer

Since the rock is dropped (not thrown), its initial velocity $v_0 = 0$. The position equation simplifies to $s = -16t^2 + s_0$, where $s_0 = 180$ feet (the height of the cliff). Setting $s = 0$ (when the rock hits the water), we get $0 = -16t^2 + 180$. Solving for $t$, we find $t \approx 3.35$ seconds.

Assume That Air Resistance Is Negligible, Which Implies That the Position