SOLUTION: calculus-rate of change A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow

Question 914105: calculus-rate of change
A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than the height of the boat's bow. The rope is being pulled in at a rate of 1 m/s. When the boat is 6 meters from the pier, how fast is the boat approaching the pier? (Give your answer correct to five decimal places.)

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than the height of the boat's bow. The rope is being pulled in at a rate of 1 m/s. When the boat is 6 meters from the pier, how fast is the boat approaching the pier? (Give your answer correct to five decimal places.)
------------------
x = boat's distance
r = rope length
Get the distance as a function of the rope length.

Differentiate wrt time.
dx/dt = (1/2)*2r*(r^2 + 1)^(-1/2)*(dr/dt)
@ r = sqrt(37):
dx/dt = sqrt(37)/sqrt(38)
=~ 0.98675 m/sec
RELATED QUESTIONS
A canoe takes a total of 16 hours to travel from the pier to the boat and back. It... (answered by JulietG)

A 12ft. rope secures a boat to a pier. The boat has an 11ft. horizontal distance from the (answered by josgarithmetic)

A jet ski with average speed of 60 mph left a pier by the river upstream. Fifteen minutes (answered by ikleyn)

A surveyor is measuring the distance across a small lake. He has set up his transit on... (answered by Theo)

A ship is approaching a harbour between a pier and a lighthouse. The distance between the (answered by ankor@dixie-net.com)

A motorboat, moving at a speed of 10 km/hour, left a pier traveling against the current... (answered by josgarithmetic)

A pier 1250 meters long extends at an angle from the shoreline. A surveyor walks to a... (answered by ankor@dixie-net.com)

A motorboat travels the distance from one pier to another pier in 4 hours and the way... (answered by josgarithmetic,greenestamps,ikleyn)

This is a weighted average problem. Hope I chose the right section.... boat number one... (answered by checkley71)