2.6 Related Rates

Related Rate Problems

General Steps for solving a Related Rate problem Set up: Draw picture/ Label now – what values do we know are fixed? ind – what are we looking for and when? quation – relate the variables ifferentiate – both sides w.r.t. independent variable (time) ubstitute/Solve Set up: Draw picture/ Label now – what values do we know are fixed? ind – what are we looking for and when? quation – relate the variables ifferentiate – both sides w.r.t. independent variable (time) ubstitute/Solve

Example 1: Volume of sphere Suppose a “spherical” balloon is being inflated so that its radius is changing at 3 cm/sec. How fast is the volume changing when the radius is 20 cm?

Example 2: “Triangular” motion Suppose a 25 ft. ladder is leaning against a wall. The foot of the ladder is being pulled away from the bottom of the wall at a rate of 14 ft. sec. At what rate is the top of the ladder moving down the wall when it is 7 ft. above the ground?

Two cars leave an intersection at the same time, one traveling north at 30 miles/hr. and the other going east at 40 miles/hr. How fast is the distance between them changing 30 minutes later?

Example 4: Right Circular Cone

Example 5: Angular Motion A winch is pulling a boat into the dock that is 20 feet above the boat’s bow. If the rope is hauled in at a rate of 2 ft/sec, how fast is the boat approaching the dock when there is 22 feet of rope still out?

Example 5: Angular Motion b) How fast is the angle between the rope and the water changing when the rope reaches 20 feet?

Example 6: filling a cone

2.6 p. 153 #5, 7, 11, 13, 15, 21, 25