Math 2413 – Calculus I
Section 2.8 Related Rates
• Idea: To compute the rate of change of one quantity in terms of the rate of change of another quantity.
• Procedure: Find an equation that relates the two quantities. Use the Chain Rule to differentiate with respect to
time.
• Rate of change of ? is
d?
dt
Ex: A spherical balloon is being deflated such that its volume decreases at a rate of 100 cm3 /s. How fast is the
radius decreasing when the diameter is 50 cm?
Math 2413
Section 2.8 Continued
Ex: A 10 ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at 1 ft/s,
how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?
Ex: Car A is traveling west at 55 mi/h and car B is traveling north at 65 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 0.9 mi and car B
is 1.2 mi from the intersection?
2
Math 2413
Section 2.8 Continued
Ex: A paper cup has the shape of a cone with height 10cm and radius 3cm (at the top). If water is poured into
the cup at a rate of 2cm3 /s, how fast is the water level rising when the water is 5cm deep?
3
Math 2413
Section 2.8 Continued
Ex: A Ferris wheel with a radius of 10m is rotating at a rate of one revolution every 2 minutes. How fast is a
rider rising when his seat is 16m above ground level?
Ex: A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline and
its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it
is 1km from P?
4