16. A spotlight on the ground shines on a wall 12 m away. If a man
2 m tall walks from the spotlight toward the building at a speed
of 1.6 m!s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
17. A man starts walking north at 4 ft!s from a point P. Five min-
utes later a woman starts walking south at 5 ft!s from a point
500 ft due east of P. At what rate are the people moving apart
15 min after the woman starts walking?
18. A baseball diamond is a square with side 90 ft. A batter hits the
ball and
runs
toward
first 1;base
with
a speed
In Class
project
sheet number:
Monday,
February
01 2016;of 24 ft!s.
Grades from this project contribute towards class participation.
(a) At what rate is his distance from second base decreasing
1. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first
when
hea speed
is halfway
base with
of 24 ft/s. to first base?
(a) At what rate is his distance from second base decreasing when he is halfway to first base?
(b) At
what rate is his distance from third base increasing at
(b) At what rate is his distance from third base increasing at the same moment?
the same moment?
90 ft
Project 1
19. The altitude of a triangle is increasing at a rate of 1 cm!min
while the area of the triangle is increasing at a rate of
ble at stewartcalculus.com
n part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
e. Cengage Learning reserves the right to remove additional content1 at any time if subsequent rights restrictions require it.
97909_03_ch03_p242-251.qk:97909_03_ch03_p242-251
9/21/10
10:26 AM
Page 249
equal. How fa
pile is 10 ft hi
2 cm2!min. At what rate is the base of the triangle changing
when the altitude is 10 cm and the area is 100 cm2 ?
In Class
project
sheet
number:
Monday,
01 2016;
20. A
boat is
pulled
into a2;dock
by aFebruary
rope attached
to the bow of
Grades from
this
project
contribute
towards
class
participation.
the boat and passing through a pulley on the dock that is 1 m
higher
bow
the attached
boat. If to
thetherope
at apassing
rate through
1. A boat is
pulledthan
into the
a dock
by of
a rope
bowisofpulled
the boatinand
a pulley on
dock how
that isfast
1 mis
higher
than approaching
the bow of thethe
boat.
If the
rope it
is is
pulled in at a
ofthe
1 m!s,
the boat
dock
when
rate of 1 m/s,
how
fast
is
the
boat
approaching
the
dock
when
it
is
8m
from
the
dock?
8 m from the dock?
21. At noon, ship A is 100 km west of ship B. Ship A is sailing
south at 35 km!h and ship B is sailing north at 25 km!h. How
fast is the distance between the ships changing at 4:00 PM?
22. A particle moves along the curve y ! 2 sin"! x!2#. As the par-
ticle passes through the point ( 13 , 1), its x-coordinate increases
at a rate of s10 cm!s. How fast is the distance from the particle to the origin changing at this instant?
23. Water
Project
2 is leaking out of an inverted conical tank at a rate of
10,000 cm !min at the same time that water is being pumped
into the tank at a constant rate. The tank has height 6 m and the
diameter at the top is 4 m. If the water level is rising at a rate
of 20 cm!min when the height of the water is 2 m, find the rate
at which water is being pumped into the tank.
3
24. A trough is 10 ft long and its ends have the shape of isosceles
triangles that are 3 ft across at the top and have a height of 1 ft.
If the trough is being filled with1water at a rate of 12 ft3!min,
how fast is the water level rising when the water is 6 inches
deep?
28. A kite 100 ft a
of 8 ft!s. At w
horizontal dec
29. Two sides of a
between them
at which the a
between the si
30. How fast is th
changing in E
from the wall?
31. The top of a la
0.15 m!s. At t
from the wall,
How long is th
; 32. A faucet is fill
with water at a
water is rising
ing facts: 1 L
sphere with ra
In Class project sheet number: 3; Monday, February 01 2016;
Grades from this project contribute towards class participation.
1. A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the
ground 20 ft from the path and is kept focused on the man. At what rate is the searchlight
rotating when the man is 15 ft from the point on the path closest to the searchlight?
Project 3
1
26 AM
Page 249
In Class project sheet number: 4; Monday, February 01 2016;
Grades from this project contribute towards
class participation.
SECTION
3.9 RELATED
RATES
249
1. Gravel is being dumped from a conveyor belt at a rate of 30 ft3 /min, and its coarseness is
such
that it How
forms afast
pile in
of a cone
whose
base
diameter andwhen
height the
are always
equal.
isthe
theshape
height
of the
pile
increasing
equal. How fast is the height of the pile increasing when the pile is 10 ft high?
pile is 10 ft high?
ate
s
w
rs
28. A kite 100
Project
4 ft above the ground moves horizontally at a speed
of 8 ft!s. At what rate is the angle between the string and the
horizontal decreasing when 200 ft of string has been let out?
29. Two sides of a triangle are 4 m and 5 m in length and the angle
between them is increasing at a rate of 0.06 rad!s. Find the rate
at which the area of the triangle is increasing when the angle
between the sides of fixed length is !!3.
1
30. How fast is the angle between the ladder and the ground
changing in Example 2 when the bottom of the ladder is 6 ft
In Class project sheet number: 5; Monday, February 01 2016;
Grades from this project contribute towards class participation.
1. Car A is traveling west at 50 mi/h and car B is traveling north at 60 mi/h. Both are
headed for the intersection of the two roads. At what rate are the cars approaching each
other when car A is 0.3 mi and car B is 0.4 mi from the intersection?
Project 5
1
In Class project sheet number: 6; Monday, February 01 2016;
Grades from this project contribute towards class participation.
1. Water is leaking out of an inverted conical tank at a rate of 10, 000 cm3 /min at the same
time that water is being pumped into the tank at a constant rate. The tank has height 6 m
and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when
the height of the water is 2 m, find the rate at which water is being pumped into the tank.
Project 6
1