The Midair Grab

An ancient artifact is thrown horizontally off of a ledge overlooking a pool of lava. It has an initial speed of v0Av_{0A} and has mass mm. There is a raised platform in the middle of the lava pool, at a distance DD to the left of the ledge, and HH 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 2m2m. He takes a running horizontal leap off his ledge at the same instant the artifact is thrown.

If v0A=20.2msv_{0A} = 20.2 \frac{m}{s}, D=15.3mD = 15.3 m, and H=10.1mH = 10.1 m, how fast [v0Iv_{0I}] must Indy leap, so that he grabs the artifact and lands safely on the platform? Give your answer in ms\frac{m}{s}, rounded to 3 significant figures.

For acceleration due to gravity, use g=9.81ms2g = 9.81 \frac{m}{s^{2}}.

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