AB Calculus - Hardtke
Name ___________________________________
Assignment 8.6: Related Rates Review
Due Date: Tuesday, 4/8
1. Complete the indicated implicit differentiation for each:
A.
B.
C.
2. Water is flowing into a cone of height = 16 cm and r = 4 cm at 2
15 cm deep?
D.
⁄
.
How fast is the water level rising when it is
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
radian/s when the
2000
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
SOLUTION KEY
Assignment 8.6: Related Rates Review
1. Complete the indicated implicit differentiation for each:
A.
B.
C.
2. Water is flowing into a cone of height = 16 cm and r = 4 cm at 2
15 cm deep?
D.
⁄
.
How fast is the water level rising when it is
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
radian/s when the
2000
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.