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.

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.

Quizplus · Accepted Answer

Taking the derivative of the given position function, we get the velocity function, V(t) = -32t-276.984. At impact, t = sqrt(1370/16) = 11.065. Substituting this value in the velocity function, we get V(11.065) = -32(11.065)-276.984 = -356.48 ft/sec, which when rounded to three decimal places gives -276.984 ft/sec. Therefore, the correct answer is option D. To find the velocity at impact, we need to find the derivative of the given position function. Taking the derivative, we get:
v(t) = -32.2t - 276.984
We want to find the velocity at the time it takes for the object to hit the ground. To do this, we set the position function equal to 0 and solve for t:
-16.1t^2 - 276.984t + 1370 = 0
Using the quadratic formula, we get t = 4.392 seconds (rounded to three decimal places).
Plugging this value into the velocity function, we get:
v(4.392) = -32.2(4.392) - 276.984 = -138.492 ft/sec
Therefore, the answer is D.

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