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 1380 feet tall.Find velocity of the coin at impact.Round your answer to the three decimal places.
A)-257.371
B)-123.207
C)-111.445
D)-246.414
E)-236.414

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 1380 feet tall.Find velocity of the coin at impact.Round your answer to the three decimal places. ​
A)-257.371 
B)-123.207 
C)-111.445 
D)-246.414 
E)-236.414

Quizplus · Accepted Answer

We know that the position function is given by 11e^-0.003x, where x is the height in feet. The initial height (when the coin is dropped) is 1380 feet, so x = 1380.

To find the velocity at impact, we need to take the derivative of the position function with respect to time.

dy/dt = d/dt (11e^-0.003x) = -0.033e^-0.003x

We can substitute x = 1380 into this equation to find the velocity at impact:

dy/dt = -0.033e^-0.003(1380) = -0.033e^-4.14 ≈ -246.414

Therefore, the velocity at impact is approximately -246.414 feet per second.

The correct answer is D.

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