Related Rates

[tdk]

Hey everyone, first time at this site and it looks pretty cool. I'm having trouble with this word problem and if anyone could help me out it would be appreciated.

Ok the question is: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s how fast is the boat approaching the dock when it is 8 m from the dock.

 

[Gene]

You have a right triangle BPD (boat, pully, dock)

BP²=1²+BD²
Take the derivitive of both sides with respect to t and solve for dBD/dt knowing dBP/dt = 1

 

[tdk]

Ok what you suggested is what I did the first time I did the question. Doing it that way gave me an answer for dBD > 1 which should not be possible. I ended up with sqrt(65) * 1 / 8.

 

[stapel]

If you are asking for further assistance or for your work to be checked, please reply showing all your steps.

Thank you.

Eliz.

 

[Gene]

When I chose dBP/dt = 1, that implied that a positive movement of the boat was toward the dock. For your reasoning (more intuitive than mine) to apply dBP/dt = -1. It should work either way, though I didn't actually carry out the computation.
-----------------
Gene