A person moves on a straight path with constant velocity u î. He observes that rain appears to fall straight downward along -ĵ. When he increases his speed to twice the original value, the rain is seen to make an angle θ with the vertical. The velocity of the rain relative to the ground

Question

A person moves on a straight path with constant velocity u î. He observes that rain appears to fall straight downward along -ĵ. When he increases his speed to twice the original value, the rain is seen to make an angle θ with the vertical. The velocity of the rain relative to the ground is

Accepted Answer

u î - (u)/(tanθ) ĵ. When the man moves at u and rain looks vertical, the rain's horizontal velocity equals u. At speed 2u the apparent horizontal component is u (backward), and tan(theta) = u/|v_y| gives |v_y| = u/tan(theta) downward. So the rain's ground velocity is u i - (u/tan(theta)) j.

A person moves on a straight path with constant velocity u î. He observes that rain appears to fall straight downward along -ĵ. When he increases his speed to twice the original value, the rain is seen to make an angle θ with the vertical. The velocity of the rain relative to the ground is

Solution

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