Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.
A) 2.849 sec
B) 10.273 sec
C) 10.693 sec
D) 3.087 sec
E) 10.091 sec

Question

Suppose the position function for a free-falling object on a certain planet is given by  . A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.
A) 2.849 sec 
B) 10.273 sec 
C) 10.693 sec 
D) 3.087 sec 
E) 10.091 sec

Quizplus · Accepted Answer

First, we need to find the value of t that makes h(t) equal to 0 (which means the coin has reached the ground).

11e^(-0.003t^2) = 1372

Divide both sides by 11:

e^(-0.003t^2) = 124.727

Take the natural logarithm of both sides:

-0.003t^2 = ln(124.727)

Solve for t:

t = sqrt(-ln(124.727)/0.003)

Using a calculator, we get t ≈ 10.693 seconds.

Therefore, the answer is C: 10.693 sec.

Suppose the Position Function for a Free-Falling Object on a Certain