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.