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. Determine the velocity function for the coin.

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. Determine the velocity function for the coin.

Quizplus · Accepted Answer

To find the velocity function, we take the derivative of the position function with respect to time:

v(t) = -32t + 160

where -32 is the acceleration due to gravity on this planet (given in the problem), and 160 is the initial velocity (the velocity of the coin when it is dropped from rest at the top of the building).

The answer choices are in the form of a position function, so we need to differentiate each choice to see which one gives us the velocity function we found above.

Differentiating choice B:

v(t) = 11e^(kt)

v'(t) = 11ke^(kt)

We want to compare v'(t) to the velocity function we found earlier:

v'(t) = 11ke^(kt) = -32t + 160

Solving for k:

k = -32/11

Substituting k back into our original equation:

v(t) = 11e^(-32/11)t

This matches the velocity function we found earlier, so the answer is B.

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