Related Rates Day 3

4.6

Two boats are approaching a buoy along paths that make a 90 degree angle. The first boat is 160 feet from the buoy and is traveling at a rate of 30 feet per second. The second boat is 135 feet from the buoy and is traveling at a rate of 35 feet per second. Find the rate of change of the distance between the boats.

An observer stands 20 feet from the base of a flagpole and watches a flag being lowered at a rate of 5 ft/sec. Determine the rate at which the angle of elevation from the observer to the flag must be changing at the instant that the flag is 15 feet above eye-level.

A camera is mounted at a point 3000 ft from the base of a rocket launching pad. If the rocket is rising vertically at 880 ft/sec when it is 4000 ft above the launching pad, how fast must the camera elevation angle change at that instant to keep the camera aimed at the rocket?

A 12 foot ladder is leaning against a house. If the bottom of the ladder is pulled away from the base of the wall at a rate of 3 ft/sec, at what rate is the angle between the ladder and the ground changing when the lower end of the ladder is 6 feet from the house?

pg 237 #1-3,9,11-14,16,17, 20-22, 24,31,35

(13,21,31,35 involve angles)

A fish is reeled in at a rate of 1 foot per second from a point 10 feet above the water. At what rate is the angle between the line and the water changing when there is a total of 25 feet of line out?