Assume that air resistance is negligible, which implies that the position equation is a reasonable model.A rock is dropped from the top of a 140-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.

Question

Assume that air resistance is negligible, which implies that the position equation  is a reasonable model.A rock is dropped from the top of a 140-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.

Quizplus · Accepted Answer

The position equation for this scenario is given as:

h(t) = -16t^2 + 140

where h(t) represents the height (in feet) of the rock at time t (in seconds) after it is dropped.

Since we want to know when the rock hits the water, we need to find the value of t when h(t) = 0 (since the height of the water is 0). So we set up the equation:

-16t^2 + 140 = 0

Solving for t, we get:

t = √(140/16) = √8.75 ≈ 2.96 seconds

Therefore, the best choice is B) 2.96 seconds.

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