A silver dollar is dropped from the top of a building that is 1363 feet tall. Us

Question

A silver dollar is dropped from the top of a building that is 1363 feet tall. Use the position function below for free-falling objects.

s(t) = 16t2 + v0t + s0

(a) Determine the position and velocity functions for the coin.

(b) Determine the average velocity on the interval [3, 4].
3   ft/s

(c) Find the instantaneous velocities when t = 3 seconds and t = 4 seconds.

(d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.)
t = 6    s

(e) Find the velocity of the coin at impact. (Round your answer to three decimal places.)
7    ft/s

Explanation / Answer

a) s(t) = -16*t^2 + 1363

v(t) = -32*t

b) Vavg = [s(4) - s(3)]/(4-3) = -112 ft/s

c) v(3) = -32*3 = -96 ft/s

  v(4) = -32*4 = -128 ft/s

d)  s(t) = -16*t^2 + 1363 = 0 =====> t = 9.23 sec

e) v(9.23) = -32*9.23 = -295.36 ft/s

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