A silver dollar is dropped from the top of a building that is 1343 feet tall. Us

Question

A silver dollar is dropped from the top of a building that is 1343 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 [2, 3].
3 ft/s

(c) Find the instantaneous velocities when t = 2 seconds and t = 3 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

Given

s(t) = 16t2 + v0t + s0

a)

For free fall

s(t) = 16t2

v(t) = dS/dt = -32t

b)

at 2s

S1 = -64 ft and

at 3s    S2 = -144 ft

average velocity

Vavg = S2 - S1 / t2 - t1

V = 80 ft/s

c)

at t = 2s

v(2) = 32 * 2 = 64 ft/s

V(3) 32 * 3 = 96 ft/s

d)

in free fall t

total time t = sqrt( 1343/16)

t = 9.16 s

e)

v = sqrt (2 * g * h)

v = 291.46 ft/s

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