A man finds that when he runs east at 10 m/s, rain appears vertically downward. When he runs east at 20 m/s, rain appears at 45° to the vertical. The magnitude of the actual vertical component of rain velocity is:
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Question

A man finds that when he runs east at 10 m/s, rain appears vertically downward. When he runs east at 20 m/s, rain appears at 45° to the vertical. The magnitude of the actual vertical component of rain velocity is:

Options

G1 Physics · Accepted Answer

When the man runs at 10 m/s and rain appears vertical, the actual horizontal component of rain must be 10 m/s east. When he runs at 20 m/s, the relative horizontal component has magnitude |10 - 20| = 10 m/s. For apparent angle 45° from vertical, horizontal and vertical relative components are equal. Thus the vertical rain component is 10 m/s. Hence option B is correct.