Summary Notes for Related Rates problems from differential calculus (MATH 184, UBC)
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Course
MATH 184
Institution
University Of British Columbia (UBC
)
Book
Calculus: Early Transcendentals
Every possible type of related rates problem that may appear on your exam has been worked through in this document. Very helpful because it shows what type of approach you should take when faced with these difficult types of problems which take many forms. Includes:
Water is leaking out of a conical tank At 500 cm³/min. The tank has a height of
24 cm and a radius of 6 cm. Find the rate at which water is being poured into the
tank if the water level is rising at 15 cm/min when the height of the water is 9cm.
SMU the water level
dh
is
rising ,
• DI IS the rate level
=
that enters
of water
Into the tank exceeds the rate
h=q
H of water that leaves the tank
H =
24
& r 6 E
notice ratio between
height 4: I
=
radius =
24
a h=4r 24=416)
r
-
-
I V= 's Trh f- It #12h
4
Oo V =
'T IT h
ddtf Igt
'
V h
Ig
=
= .
3h 2. DI
dt
du
Te
=
Tig °
IT .
3195 .
lls )
# =
V' in -
V' out
d¥ =
IT .
1215
16
✓ DI
'
out =
-
500 = 238.56
dt
238.56 =
Vin -
500
V' in = 738.56
Simultaneity
'
Water
'
is
being poured In @ rate of 738.56cm Im in 1h ,
500cm Im in flows So tank 238
'
out net of 56cm Im in
.
,
gains a .
, A 13 feet ladder is leaning against a house. The ladder slides down the wall at a rate
of 3 ft/min. How fast is the ladder moving away from the base of the wall when the
foot of the latter is currently 5 ft from the wall?
Y ? 52
' ' '
of
=
y ez t
y 13 12
+
y
-
-_ =
=
1=13
µ
X=s If =-3
FI = ? =-3
'
Ii = ?
⇐ Cx
Y
-15=11*91%17.7 : !÷:
.
shame .
2x .
II t
2g It
. =
0 215 ) .IE ,
+2112) .
-
3=0
5
×
10 -
II -
72=0 fit =
351=7.2 ftlmin
How fast is the area of the triangle changing?
Area D=
of BIH
⇐ ( A- ( Xy)
'
X. y
) (2) (
Xy) 121
'
A-
-
= =
-2 .
2
# ' 2)
=¥igt¥;¥H= Its 35¥
3)
IF
' ' -
= =
35.7 =
How fast is the angle between ladder and the ground changing?
* Hottel 'm't # in
(
'
.
SOH
#
FAH TOA =o+ He )
l Sth
-
-
tf I -
-
Ft( Sino F ) -
-
13 O
my coso.IT?-- f. fit ¥ .
=
( Ee)
need to find O
⑦
TIA 5 daff
- =
Cos @
=f=E
5 (5/13)
'
O COS
-
=
}
0=67.380
×
d§
-
=
radians linin
,
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