# Two chests connected by a rope in tension

## Homework Statement

Two chests are connected by a 15 meters long rope attached to a ceiling hook hanging 4 meters high. The chest (1) at 5 meters from the hook has a velocity of 1/2 m/s away from the other chest (2). The chests remain flat on the ground and the rope is under tension.
What is the speed of the other chest?

## The Attempt at a Solution

Let c1,2 be the chests, let h be the hook, let centre be the perpendicular projection of the hook on the ground.
We know the distance c1-centre (right triangle) at any time (1/2 m/s). We also know the distance c1-h (right triangle), h-c2 (length of the rope), hence we know the distance c2-centre (right triangle) at any time. The time derivative of this function at t=0 solves the problem.
Is there a shortcut, another approach? Can you think of any interesting physical or mathematical considerations? I don't think my solution is very satisfactory.

Due to the Darwinian environment of this forum and with all the heavy competition going on, I'd like to bring my post back to the top of the food chain.
Perhaps my question is a little too vague?

pbuk
Gold Member
There are two right angled triangles and for each you know the hypotenuse and base length. In time δt the base of one of the triangles changes by a certain factor, and therfore the whole triangle is scaled by that factor. Can you see how to work out the scaling factor for the other triangle in that time?

Scaled triangles? The h(eight) of the two triangles is a constant, but it's an interesting take on a different problem.

pbuk
Gold Member
The h(eight) of the two triangles is a constant
Oops, that's a good point.

haruspex