Post a New Question

Math-Calculus

posted by .

Consider two ships which are joined by a cable attached to each ship at the water line. Suppose the two ships are 200 metres apart, with the cable stretched tight and attached to a pulley which is anchored halfway between the ships at a depth of 45 metres. If one ship moves away from the other at 3 km/h,how quickly is the other ship moving after one minute?

I'm totally stuck...

  • Math-Calculus -

    Draw a diagram. Label as P the point on the ocean directly above the pulley. If the ship being pulled is x meters from P, and the pulling ship is at distance y,

    √(x^2+45^2) + √(y^2+45^2) = 200

    3 km/hr = 50m/min, so we want
    dx/dt when t=1 and dy/dt=50.

    at t=0, x=y=89.30
    after 1 minute, y=139.30, so x=29.14

    x/√(x^2+45^2) dx/dt + y/√(y^2+45^2) dy/dt = 0

    29.14/53.61 dx/dt + 139.30/146.39 * 50 = 0
    dx/dt = -87.53 m/s = 5.25 km/hr

    Note that this cannot continue for long, as the ship will be pulled under by the cable.

Answer This Question

First Name
School Subject
Your Answer

Related Questions

More Related Questions

Post a New Question