Related Rates Worksheet Chap:5 assign: 73ic 1. When a circular plate of metal is heated in an oven, its radius increases at a rate of .001 cm

sec. At what rate is the plate’s area

increasing when its radius is 50 cm ?

2. A hot-air balloon straight up from a level field is tracked by a range finder 500 m from the balloon’s lift off point. At the moment the range finder’s angle of elevation is π

4, the

angle is changing at a rate of .114 radmin

. How fast is the

balloon rising at that moment?

3. The radius, r, and the surface area, S, of a sphere are related by S = 4πr2 Write an equation that relates dS

dt to dr

dt.

4. The radius, r, height, h, and volume, V, of a right circular cylinder are related by the equation V = πr2h . a. How is dV

dt related to dh

dt if r is a constant?

b. How is dVdt

related to drdt

if h is a constant?

c. How is dVdt

related to drdt

and dhdt

if neither r and h are constant?

5. A spherical balloon is being inflated by pumping air in at a rate of

10 cm3

sec. How fast is the radius changing at the instant r = 5 cm ?

6. Water is pumped into a cone-shaped tank at a

rate of 9 m3

min. The tank stands vertex down and

has a height of 10 m. The radius at the top is 5 m. How fast is the water level rising at the instant the water is 6 m deep?

7. A road and a railroad track cross at right angles. The train is heading south at 60 mph. The car is moving east. When the train is .6 mi north of the intersection and the car is .8 mi east of the intersection, the distance between them is increasing at 20 mph. How fast is the car moving?

8. Two truck convoys leave a depot. Convoy A heads due east at 30 mph and Convoy B travels north at 40 mph. How fast is the distance between the convoys changing when, 6 minutes later, Convoy A is 4 miles from the depot and Convoy B is 3 miles from the depot? 9. A 13-ft ladder is leaning against a house when the base starts to slide away from the bottom of the wall. At the instant the base is 12 ft from the wall, the base is moving at 5 ft

sec.

a. How fast is the top of the ladder sliding down the wall at that instant? b. How fast is the area of the triangle formed by the ladder, the ground, and the wall changing at that same instant? 10. Two ships are headed away from point O along routes that are 120˚ apart from each other. Ship A moves at 14 knots (nautical miles per hour). Ship B moves at 21 knots. How fast are the ships moving apart when OA=5 miles and OB=3 miles? A nautical mile, btw, is a minute of arc on the planet Earth. A nautical mile is 1.1508 miles or 6,076 feet.