Answer to Question #147372 in Calculus for Sean

Question

In an opera house, the base of a chandelier is 160 ft above the floor. Suppose the Phantom of
the Opera dislocates the chandelier and causes it to fall from rest and crash on the floor.
a. What is the equation of motion of the chandelier?
b. Find the instantaneous velocity of the chandelier at 1 sec and 1.5 sec.
c. Find how long it takes the chandelier to hit the floor.
d. What is the speed of the chandelier when it hits the floor?

Answer 1

a) Since the initial speed is 0, equation of motion of the chandelier is

$y=y_0-\frac {gt^2} {2}=160-\frac {32.17*t^2} {2}$ for height

$v=gt=32.17*t$ for absolute speed(how much ft in any direction the chandelier will fly)

if you need speed in coordinate system speed is $v=-gt=-32.17*t$ (becasuse the chandelier fall)

b)at 1 sec: $v=32.17*1=32.17$ ft/s

at 1.5 sec: $v=32.17*1.5=48.26$ ft/s

c) to find how long it takes the chandelier to hit the floor, need to solve the equation:

$160-\frac {32.17*t^2} {2}=0$

$t^2=9.95$

$t=3.15$

d) $v=32.17*3.15=101.34$ ft/s