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GR0877 Problem 56

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (D) To fly due north a pilot should point the plane in such a direction that $\mathbf{v + u} \parallel SN$, where $\mathbf{v}$ is the velocity of the plain in still air, $\mathbf{u}$ is the velocity of the wind, and SN is the south-north line. According to the velocity addition formula, the velocity of the plane in the north direction is $\mathbf{V} = \mathbf{v + u}$, $\mathbf{V} \perp \mathbf{u}$. From this we have $(\mathbf{V} - \mathbf{u})^2 = (\mathbf{v})^2$, $V^2 + u^2 = v^2$, $V = \sqrt{v^2 - u^2}$, $t = L/V = L/\sqrt{v^2 - u^2} =$ $500/\sqrt{200^2 - 30^2} =$ $=50/\sqrt{400-9} =$ $50/\sqrt{391}$ (h).

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