9.
1/2 points |
Previous Answers
A ladder
22
feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3
feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter
has climbed up 6 feet of the ladder, the ladder makes an angle of
π
/3 with the ground. Answer the two
related rates questions below. (Hint: Use two carefully labeled similar right triangles.)
(a) If
h
is the height of the firefighter above the ground, at the instant the angle of the ladder
with the ground is
π
/3, find
dh/dt=

(b) If
w
is the horizontal distance from the firefighter to the wall, at the instant the angle of the
ladder with the ground is
π
/3, find
dw/dt
=

6/5/2019
hw17S3.9
6/6
10.
3/3 points |
Previous Answers
(Old Final Exam ProblemSp2009)
An hourglass is made up of two glass cones connected at their tips. Both cones have radius 1 inch and
height 3 inches. When the hourglass is flipped over, sand starts falling to the lower cone.
(a) When the sand remaining in the
upper cone
has height
y
inches, its volume
A
in terms of
y
is
$$π
y
327
.
(b) When the sand in the
lower cone
has reached a height of
h
inches, its volume
B
in terms of
h
is
$$π−π·(3−
h
)327
. (Hint:
B
is the volume of the bottom cone minus the volume of the empty space above the
sand.)
(c) Assume the total volume of sand in the hourglass is 3
π
/4 cubic inches. Also, assume the
height of the sand in the upper cone is decreasing at a rate of
8
/100 inches per second. At the
instant when the sand in the lower cone is 1 inch high, the height of the sand in the lower cone is
increasing at a rate of
$$.0232
inches per second.