A rocket sled is to be slowed from an initial speed of \(300 \mathrm{~m} / \mathrm{s}\) by lowering a scoop into a water trough. The scoop is \(0.3 \mathrm{~m}\) wide; it deflects the water through \(150^{\circ}\). The trough is \(800 \mathrm{~m}\) long. The mass of the sled is \(8000 \mathrm{~kg}\). At the initial speed it experiences an aerodynamic drag force of \(90 \mathrm{kN}\). The aerodynamic force is proportional to the square of the sled speed. It is desired to slow the sled to \(100 \mathrm{~m} / \mathrm{s}\). Determine the depth \(D\) to which the scoop must be lowered into the water.

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30 < Water trough P4.112 Rail