Rain falls vertically downward with speed v. An inclined plane making angle α above the horizontal moves horizontally with speed u. The magnitude of the component of rain velocity relative to the plane normal to its surface is:
Options

Question

Rain falls vertically downward with speed v. An inclined plane making angle α above the horizontal moves horizontally with speed u. The magnitude of the component of rain velocity relative to the plane normal to its surface is:

Options

G1 Physics · Accepted Answer

Take the plane velocity as uî and rain velocity as -vĵ. Then relative rain velocity is v⃗_RP = -uî - vĵ. A unit normal to the plane can be chosen as n̂ = -sinα î + cosα ĵ. Thus v⃗_RP·n̂ = u sinα - v cosα. Its magnitude is |v cosα - u sinα|. Hence option A is correct.