The Midair Grab

Classical Mechanics Level 4

An ancient artifact is thrown horizontally off of a ledge overlooking a pool of lava. It has an initial speed of \(v_{0A}\) and has mass \(m\). There is a raised platform in the middle of the lava pool, at a distance \(D\) to the left of the ledge, and \(H\) below the ledge. The artifact is going to overshoot the platform.

Indiana Jones is standing on a ledge opposite the first ledge, at the same distance from the platform and the same elevation as the first ledge. He has mass \(2m\). He takes a running horizontal leap off his ledge at the same instant the artifact is thrown.

If \(v_{0A} = 20.2 \frac{m}{s}\), \(D = 15.3 m\), and \(H = 10.1 m\), how fast [\(v_{0I}\)] must Indy leap, so that he grabs the artifact and lands safely on the platform? Give your answer in \(\frac{m}{s}\), rounded to 3 significant figures.

For acceleration due to gravity, use \(g = 9.81 \frac{m}{s^{2}}\).


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