# Using Implicit Differentiation to Solve Related Rates Problems - Page 5

Questions

- A man standing on a wharf is hauling in a rope attached to a boat, at the rate of 4 ft/sec. if his hands are 9 ft. above the point of attachment, what is the rate at which the boat is approaching the wharf when it is 12 ft away?
- Determine how fast the length of an edge of a cube is changing at the moment when the length of the edge is #5 cm# and the volume of the cube is decreasing at a rate of #100 (cm^3)/sec#?
- A collapsible spherical tank is being relieved of air at the rate of 2 cubic inches per minute. At what rate is the radius of the tank changing when the surface area is 12 square inches?
- Andy is 6 feet tall and is walking away from a street light that is 30 feet above ground at a rate of 2 feet per second. How fast is his shadow increasing in length?
- A conical cup of radius 5 cm and height 15 cm is leaking water at the rate of 2 cm^3/min. What rate is the level of water decreasing when the water is 3 cm deep?
- If a cylindrical tank with radius 5 meters is being filled with water at a rate of 3 cubic meters per minute, how fast is the height of the water increasing?
- A can of soda measures 2.5 inches in diameter and 5 inches in height. If a full-can of soda gets spilled at a rate of 4 in^3/sec, how is the level of soda changing at the moment when the can of soda is half-full?
- A water tank has the shape of an upright cylinder. The cylinder is filling at a rate of 1.5 m^3 / minute. If the tank has a radius of 2 m, at what rate is the water level increasing when the water is 3.2 m deep?
- The volume of a cube is increasing at the rate of 20 cubic centimeters per second. How fast, in square centimeters per second, is the surface area of the cube increasing at the instant when each edge of the cube is 10 centimeters long?
- The altitude of a triangle is increasing at a rate of 1.5 cm/min while the area of the triangle is increasing at a rate of 5 square cm/min. At what rate is the base of the triangle changing when the altitude is 9 cm and the area is 81 square cm?
- If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, how do you find the rate at which the diameter decreases when the diameter is 12 cm?
- A person 1.8m tall is walking away from a lamppost 6m high at the rate 1.3m/s. At what rate is the end of the person's shadow moving away from the lamppost?
- A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 13 km and climbs at an angle of 20 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 5 minutes later?
- At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the instant when the surface area is 4 square meters and the radius is increasing at the rate of 1/6 meters per minute?
- If the rate at which water vapor condenses onto a spherical raindrop is proportional to the surface area of the raindrop, show that the radius of the raindrop will increase at a constant rate?
- A beacon on a lighthouse is one mile from shore, and revolves at 10PI Radians per minute. What is the speed with which the light sweeps across the straight shore as it lights the sand 2 miles from the lighthouse?
- What is the total amount of water supplied per hour inside of a circle of radius 8 if a sprinkler distributes water in a circular pattern, supplying water to a depth of #e^-r# feet per hour at a distance of r feet from the sprinkler?
- Calculus, Optimization: Ship A is 60 miles south of ship B and is sailing North at a rate of 21 mph. If ship B is sailing west at a rate of 22 mph, in how many hours will the distance between the two ships be minimized?
- A balloon rises at the rate of 8 ft/sec from a point on the ground 60 ft from the observer. How do you find the rate of change of the angle of elevation when the balloon is 25 ft above the ground?
- Can someone explain related rates problems to me?