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 1370 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.
A) -286.705 ft/sec
B) -138.492 ft/sec
C) -111.041 ft/sec
D) -276.984 ft/sec
E) -261.984 ft/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 1370 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.
A) -286.705 ft/sec 
B) -138.492 ft/sec 
C) -111.041 ft/sec 
D) -276.984 ft/sec 
E) -261.984 ft/sec

Quizplus · Accepted Answer

The velocity of the object is given by the derivative of its position function with respect to time:

v(t) = -32t - 256

We can find the time it takes for the coin to reach the ground by setting the position function equal to zero and solving for t:

11e^(-0.00081t^2) = 1370

e^(-0.00081t^2) = 1370/11

-0.00081t^2 = ln(1370/11)

t^2 = -ln(1370/11)/0.00081

t ≈ 8.84 seconds

Now we can substitute this time into the velocity function to find the velocity at impact:

v(8.84) = -32(8.84) - 256

v(8.84) ≈ -276.984 ft/sec

Therefore, the answer is D) -276.984 ft/sec.

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