# The Midair Grab

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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