Discover the Boat's Speed: Solving for dc/dt on a Pier with 6m of Rope Out

[asz304]

A man on a pier pulls in a rope attached to a small boat at the rate of 0.4 metres
per second. If his hands are 3 metres above the place where the rope is attached,
how fast is the boat approaching the pier when there is 6 metres of rope out?


Is the question asking for dc/dt ? c is the hypotenuse.

 

[Pyroadept]

Think again about how you are setting up the triangle. Look at it from a 'side-on' view i.e. you are seeing the side of the man's face, as opposed to viewing it from the front.

Which piece represents the hypotenuse? Is it the height of the man's hand from the water, the rope, or the water? What do the other two sides of the triangle represent?

 

[asz304]

Yeah? Well the height "y" is fixed is equivalent to 3, and dx/dt is unknown, dc/dt= 0.4, right?

 

[Mark44]

No, dc/dt = -0.4. The rope is being pulled in (getting shorter), not being let out.