RELATED RATE OF CHANGE WORD PROBLEMS WORKSHEET

Problem 1 :

An airplane is flying towards a radar station at a constant height of 6 km above the ground. If the distance s between the airplane and the radar station is decreasing at a rate of 400 km per hour when s = 10 km, what is the horizontal speed of the plane ?

Solution

Problem 2 :

A light is on the ground 20 m from building. A man 2 m tall walks from the light directly toward the building at 1 m/s. How fast is the length of his shadow on the building changing when he is 14 m from the building ?

Solution

Problem 3 :

A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm³/sec. How fast is the water dropping when the height of the water is 3 cm?

Solution

Problem 4 :

Air is escaping from a spherical balloon at the rate of 2 cm³ per minute. How fast is the surface area shrinking when the radius is 1 cm?

V = 4/3 πr³ and S = 4πr²

where V is the volume and S is the surface area, r is the radius.

Solution

Problem 5 :

A funnel in the shape of an inverted cone is 30 cm deep and has a diameter across the top of 20 cm. Liquid is flowing out of the funnel at the rate of 12 cm³ /sec. At what rate is the height of the liquid decreasing at the instant when the liquid in the funnel is 20 cm deep?

Solution

Problem 6 :

Find the rate of change of the area A, of a circle with respect to its circumference C.

Solution

Problem 7 :

A boat is being pulled into a dock by attached to it and passing through a pulley on the dock, positioned 6 meters higher than the boat. If the rope is being pulled in at a rate of 3 meters/sec, how fast is the boat approaching the dock when it is 8 meters from the dock?

Solution