A man runs up a fixed inclined plane making 37° with the horizontal at 10 m/s. Rain falls vertically downward at 20 m/s. Take sin37° = 3/5 and cos37° = 4/5. The magnitude of the component of rain velocity relative to the man parallel to the inclined plane is:
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Question

A man runs up a fixed inclined plane making 37° with the horizontal at 10 m/s. Rain falls vertically downward at 20 m/s. Take sin37° = 3/5 and cos37° = 4/5. The magnitude of the component of rain velocity relative to the man parallel to the inclined plane is:

Options

G1 Physics · Accepted Answer

The man's velocity is v⃗_M = 10(cos37° î + sin37° ĵ) = 8î + 6ĵ. Rain velocity is v⃗_R = -20ĵ, so v⃗_RM = -8î - 26ĵ. A unit vector up the plane is t̂ = (4/5)î + (3/5)ĵ. Thus v⃗_RM·t̂ = -8(4/5) - 26(3/5) = -32/5 - 78/5 = -110/5 = -22 m/s. Magnitude = 22 m/s. Hence option D is correct.