Related Rates Practice

A ladder is 10 meters long and is leaning against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 2 m/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 meters from the wall?

• -1.5 m/s

• -2 m/s

• 3 m/s

• 0.5 m/s

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.SRT.C.8

A conical tank is being filled with water at a rate of 3 cubic meters per minute. If the tank has a height of 10 meters and a radius of 5 meters, how fast is the water level rising when the water is 6 meters deep?

• ~ 1/20 m/min

• ~ 1/10 m/min

• ~ 1/40 m/min

• ~ 1/30 m/min

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

Two cars are approaching an intersection. Car A is 2 km south of the intersection and moving north at 60 km/h, while Car B is 3 km east of the intersection and moving west at 80 km/h. How fast is the distance between the cars changing when Car A is 2 km from the intersection and Car B is 3 km from the intersection?

• The distance between the cars is decreasing at a rate of 55 km/h.

• The distance between the cars is decreasing at a rate of 70 km/h.

• The distance between the cars is decreasing at a rate of 85 km/h.

• The distance between the cars is decreasing at a rate of 100 km/h.

Tags

CCSS.HSG.SRT.C.8

CCSS.HSG.SRT.D.11

CCSS.HSN.VM.A.3

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 meter higher than the bow of the boat. If the rope is being pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 meters from the dock?

• about 1 m/s

• about 1.5 m/s

• about 2 m/s

• about 2.5 m/s

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.SRT.C.8

A plane is flying horizontally at an altitude of 5 km and passes directly over a radar station. If the plane is flying at a speed of 800 km/h, how fast is the distance between the plane and the radar station increasing when the plane is 10 km away from the station (direct, diagonal distance)?

• 522 km/h

• 610 km/h

• 693 km/h

• 751 km/h

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

A cylindrical tank with a radius of 4 meters is being filled with water at a rate of 2 cubic meters per minute. How fast is the water level rising when the water is 3 meters deep?

• The water level is rising at a rate of 0.04 meters per minute.

• The water level is rising at a rate of 0.08 meters per minute.

• The water level is rising at a rate of 0.12 meters per minute.

• The water level is rising at a rate of 0.16 meters per minute.

Tags

CCSS.HSG.GMD.A.3

An ice cube is melting in a way such that every side is shrinking at a rate of 1 inch/minute. At what rate is the volume decreasing when the edges of the cube are 4 inches long?

• -32 m/s

• -48 m/s

• -56 m/s

• -68 m/s

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

A snowball is melting in such a way that its volume is decreasing at a rate of 2 cubic centimeters per minute. If the snowball is a perfect sphere, how fast is the radius decreasing when the radius is 5 cm?

• -0.0038 cm/min

• -0.0064 cm/min

• -0.0081 cm/min

• -0.0099 cm/min

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1