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) Velocity is as a function of t is

v(t) =ds/dt

Here s(t)=-16t2+vot+so

v(t)=-32t+vo

b)average velocity

vavg=[s(4)-s(3)]/(4-3)

vavg=[-16(42) + 16(32)]/1 here vo=0,so=0

vavg=-112 ft/s

c) v(4) =-32(4)+ vo   and vo=0

v(4)=-128 ft/s

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

d) time of flight for free body is

t=sqrt(2h/g)

Here h=1363 ft ,g=32.2 ft/s2

t=sqrt(2x1363/32.2)=9.201 s

e) v(t) =-32t+vo   here vo=0 and t=9.201 s

v(final)=-32(9.201)=-294.432 ft/s

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