A fixed inclined plane makes 30° with the horizontal. A man starts from rest and accelerates down the plane with constant acceleration 4 m/s². Rain falls vertically downward at 20 m/s. At what time will the velocity of rain relative to the man be perpendicular to the inclined plane?
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Question

A fixed inclined plane makes 30° with the horizontal. A man starts from rest and accelerates down the plane with constant acceleration 4 m/s². Rain falls vertically downward at 20 m/s. At what time will the velocity of rain relative to the man be perpendicular to the inclined plane?

Options

G1 Physics · Accepted Answer

For the apparent rain to be perpendicular to the plane, its relative velocity component parallel to the plane must be zero. The component of rain velocity down the plane is 20 sin30° = 10 m/s. The man's speed down the plane after time t is at = 4t. Hence the relative parallel component is 10 - 4t. Setting it to zero: 10 - 4t = 0, so t = 2.5 s. Therefore option B is correct.