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.

Similar Questions

1. angle

1.) From the top of a lighthouse 52 metres high,the angles of depression of two ships due north of it are 42 and 37. How far apart are the ships ?
2. geometry

a zip line consists of a pulley attached to a cable that is strung at an angle between two objects. in the zip line at the right one end of the cable is attached to a tree. the other end is attached to a post parallel to the tree. …

A helicopter is lifting two crates simultaneously. One crate with a mass of 151 kg is attached to the helicopter by cable A. The second crate with a mass of 79 kg is hanging below the first crate and attached to the first crate by …

A helicopter is lifting two crates simultaneously. One crate with a mass of 151 kg is attached to the helicopter by cable A. The second crate with a mass of 79 kg is hanging below the first crate and attached to the first crate by …

A helicopter is lifting two crates simultaneously. One crate with a mass of 151 kg is attached to the helicopter by cable A. The second crate with a mass of 79 kg is hanging below the first crate and attached to the first crate by …
6. Math

A telephone pole is secured with two cables. The first cable is attached to the top of the pole and makes an angle of 70° with the ground. The cable is secured to the ground 8 m from the bottom of the pole. The second cable is attached …
7. Physics

Joe wishes to hang a sign weighing 730 N so that cable A, attached to the store, makes a 30.0° angle, as shown below. Cable B is horizontal and attached to an adjoining building. What is the tension in cable B?
8. Calculus

A cable hangs between two poles of equal height and 40 feet apart. At a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is h(x)=10+(0.4)(x^1.5). …
9. Math

Two ships leave a lighthouse from opposite directions.The speed of ship A is 8 Km/h faster than ship B. at the end of 60 hours the two ships are 4320 km apart. Find the speed of two ships
10. calculus

A cable hangs between two poles of equal height and 40 feet apart. At a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is h(x) = 10+(0.1)*(x^1.5). …

More Similar Questions