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Related Rates
Worksheet For each related rates
problem
below, try to use the following strategies (found on pg. 267 of your
text with
slight changed for numbers 6 and 7): 1.
Read the problem carefully 2.
Draw a diagram if possible. 3.
Introduce notation. Assign symbols
to all quantities that are functions of time. 4.
Express the given
information and the required rate in terms of
derivatives. 5.
Write an equation that
relates the various quantities of the
problem. If necessary, use the geometry
of the situation to eliminate one of the variables by substitution. 6.
Use the Chain Rule to
differentiate
into the resulting equation. (also,
think implicit differentiation) 7.
Solve for the unknown rate. The following problems are
exercises from your textbook. 1.
Suppose oil spills from a
ruptured
tanker and spreads in a circular pattern.
If the radius of the oil spill increases at a constant
rate of 1 m/s,
how fast is the area of the spill increasing when the radius is 30m? 2.
A street light is mounted
at the
top of a 15-ft-tall pole. A man 6ft tall
walks away from the pole with a speed of 5ft/sec along a straight path. How fast is the tip of his shadow moving when
he is 40ft from the pole? 3.
A man starts walking north
at
4ft/sec from a point P. Five minutes
later a woman starts walking south at a rate of 5ft/sec from a point
500 ft due
east of P. At what rate are the people
moving apart 15 minutes after the woman starts walking? 4.
The altitude of a triangle
is
increasing at a rate of 1cm/min while the area of the triangle is
increasing at
a rate of 2cm2/min. At what
rate is the base of the triangle changing when the altitude is 10cm and
the
area is 100cm2? |