AB Calculus - Hardtke Assignment 8.6: Related Rates Review Name ___________________________________

Due Date: Tuesday, 4/8 1. Complete the indicated implicit differentiation for each:

A.

B.

C.

D.

2. Water is flowing into a cone of height = 16 cm and r = 4 cm at 2

⁄ . How fast is the water level rising when it is

15 cm deep?

3. If air is pumped into a spherical balloon so its volume increases at a rate of 100

⁄ How fast is the radius of the balloon increasing when the diameter is 30 cm?

4. A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6ft from the wall?

Over

5. At noon ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00pm?

6. A hot air balloon is rising vertically. An observer on the ground is 2000 m from the point where the balloon took off.

The angle between the ground and the observer's line of sight increases at a rate of 1

2000radian/s when the

balloon reaches a height of 3000 meters. How fast is the balloon rising at that moment?

7. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

AB Calculus - Hardtke Assignment 8.6: Related Rates Review SOLUTION KEY

1. Complete the indicated implicit differentiation for each:

A.

B.

C.

D.

2. Water is flowing into a cone of height = 16 cm and r = 4 cm at 2

⁄ . How fast is the water level rising when it is

15 cm deep?

4. If air is pumped into a spherical balloon so its volume increases at a rate of 100

⁄ How fast is the radius of the balloon increasing when the diameter is 30 cm?

4. A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6ft from the wall?

Over

5. At noon ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00pm?

6. A hot air balloon is rising vertically. An observer on the ground is 2000 m from the point where the balloon took off.

The angle between the ground and the observer's line of sight increases at a rate of 1

2000radian/s when the

balloon reaches a height of 3000 meters. How fast is the balloon rising at that moment?

7. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.