Question

 

part 1)

A road perpendicular to a highway leads to a farmhouse located 1 mile away. An automobile traveling on the highway passes through this intersection at a speed of 65mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 6 miles past the intersection of the highway and the road? The distance between the automobile and the farmhouse is increasing at a rate of miles per hour.

part 2)

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 10 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 20 ft/min, at what rate will the boat be approaching the dock when 110 ft of rope is out?

The boat will be approaching the dock at  ft/min.

Hint: Sketch a diagram of this situation.

part 3)

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 mi2/hrmi2/hr. How rapidly is radius of the spill increasing when the area is 10 mi2mi2?

The radius is increasing at  mi/hr.

part 4)

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 6 PM?

The distance is changing at  knots.

(Note: 1 knot is a speed of 1 nautical mile per hour.)

part 5)

A spherical balloon is inflated so that its volume is increasing at the rate of 3.8 ft3/minft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.8 feet?

The diameter is increasing at  ft/min.

Answer 1