University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2021
Views:

464

Pages:

2
Author:

Elise Donaldson

Calculus AB Related Rates Worksheet #1 Name ____________________________________ Provide a neat, clear, and well-organized analysis of each of the following problems. Where appropriate, draw a diagram. Show all formulas involved and all steps in the differentiation. Make sure to provide proper units. 1. The height of an object at time t is given by the equation h = −2t 3 + 6t 2 + 10 where the height is measured in feet and the time in seconds. a) What is the velocity when t = 3? b) What is the velocity when the acceleration is 0? c) When is the velocity 6? 2. The radius of a spherical balloon is increasing at a rate of 3 ft/min. How fast is the volume increasing when the radius is 2 ft? 3. The top of a 10 ft ladder is sliding down a wall at the rate of 3 ft/sec. How fast is the bottom of the ladder sliding along the ground when the top is 6 ft from the ground? 4. A conical water tank has a radius of 3 m and a height of 6 m. Water is flowing into the tank at the rate of 12 cubic meters per min. How fast is the water level rising when the water is 2 m high? 5. One car leaves point X at noon traveling north at 20mph. A second car leaves point X at 1:00 pm traveling east at 40 mph. How fast is the distance between the cars increasing at 3:00 pm? 6. A point travels along the curve y = x 3 − x . Find dy dx = 3 cm/sec. when x = 2 cm and dt dt 7. A plane flying at an altitude of 12 miles passes directly over a person standing on the ground. The plane is traveling at 500 mph. How fast is the distance between the person and the plane increasing 36 seconds later? 8. A man leaves point A at 2:00 pm and walks south at 4 mph. At 2:30 pm a second man leaves the same point and walks east at 3 mph. How fast is the distance between the two men increasing at 3:30 pm? 9. An airplane flying horizontally at an altitude of 1 mile passes directly over an observer. The plane is flying at 240 mph. How fast is the distance between the plane and the observer changing 30 seconds later? 10. A 20 ft ladder is leaning against the wall. The bottom of the ladder is pulled along the level ground at 2 ft/sec. How fast is the top of the ladder moving down the wall when the foot of the ladder is 4 ft from the wall? 11. A girl is flying a kite at a constant height of 300 ft. The kite is moving horizontally away from her at a rate of 25 ft/sec. How fats must she let the string out when the kite is 500 ft away from her? Answers: 1. a. 18 ft/sec backward b. 6 ft/sec c. 1 sec ft 3 min 2. 48 3. 4. 9 ft/sec 4 12  m/min 5. 44 mph 6. 33 cm/sec 7. 8. 9. 2500 mph 13 11  4.92 mph 5 480 5 10. −  214.66 mph 1 6  −0.408 ft/sec 11. 20 ft/sec