Question

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...

Answer 1

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.