Related Rates
1. A conical tank with vertical axis of symmetry, open at the top and with vertex at the bottom, has base radius 4 ft. and altitude 10 ft. If water is flowing into the tank at 9 cubic ft per min, how fast is the level rising when the water is 5 ft. deep?
2. A ladder 26 ft long is leaning against a vertical wall. If the bottom of the ladder is pulled horizontally away from the wall at a uniform rate of 2 ft. per sec, what is the velocity of the top of the ladder when the lower end is 24 ft. from the wall?
3. A woman 5 ft tall walks at the rate of 4 ft. per sec. directly away from a lamp that is 15 ft. tall. Find the rate at which the end of her shadow is moving when she is 30 ft. away from the base of the lamp post.
4. An automobile traveling at a rate of 60 ft. per second is approaching n intersection. When the automobile is 1200 ft. from the intersection, a second automobile moving at a rate of 40 ft. per second crosses the intersection traveling in a direction at right angles to the path of the first vehicle. How fast are the two automobiles separating 10 seconds after the second vehicle crosses the intersection?
5. A right circular cylinder has a constant height of 5 in. If the volume is increasing at the rate of 8 cubic inches per min, how fast is the lateral surface area increasing when the radius of the base is 4 inches.
6. A cone of radius r centimeters and height h centimeters is lowered point first at a rate of 1cm/s into a tall cylinder of radius R centimeters that is partially filled with water. How fast is the water level rising at the instant the cone is completely submerged?
7. The minute hand on a watch is 8mm ling and the hour hand is 4mm long. How fast is the distance between the tips of the hands changing at 1 o’clock?
Ans: 1. 9/4pi ft/min 2. -4.8 ft/sec 3. 6ft/sec 4. 27.7 ft/sec 5. 2 inches sqr/min