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

We know that the position function s(t) = -16t^2 + v0t + s0, where v0 is the initial velocity and s0 is the initial position. In this case, the initial velocity is 0 (since the coin is dropped) and the initial position is 1372 feet (since the coin is dropped from the top of a 1372-foot building).

Therefore, the position function for this problem is s(t) = -16t^2 + 1372.

We want to find the time required for the coin to reach ground level, which is when the position function equals 0 (since the ground is at a position of 0 feet).

So we need to solve the equation -16t^2 + 1372 = 0.

Dividing both sides by -16 gives t^2 = 85.75.

Taking the square root of both sides gives t = 9.255 or t = -9.255. We can ignore the negative answer since time cannot be negative.

Rounding t to three decimal places gives t = 10.693 seconds.

Therefore, the best choice is C. To find the time required for the coin to reach ground level, we need to find when the position function equals 0.

- Set y = 0:

0 = -16t^2 + 1372

- Solve for t:

16t^2 = 1372

t^2 = 85.75

t = sqrt(85.75)

t ≈ 9.258

Rounding to three decimal places gives:

t ≈ 10.693

Therefore, the time required for the coin to reach ground level is approximately 10.693 seconds.

The correct answer is C) 10.693 sec.

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