When a car is at rest, its driver sees rain falling vertically. When the car moves with speed v, the apparent rain makes 60° with the horizontal. When the speed is increased to (1+β)v, the apparent angle becomes 45°. The value of β is closest to:
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Question

When a car is at rest, its driver sees rain falling vertically. When the car moves with speed v, the apparent rain makes 60° with the horizontal. When the speed is increased to (1+β)v, the apparent angle becomes 45°. The value of β is closest to:

Options

G1 Physics · Accepted Answer

Let rain's vertical speed be V. At car speed v, tan60°=V/v, so V=√3v. At speed (1+β)v, tan45°=V/[(1+β)v]=1. Hence 1+β=√3, so β=√3-1≈0.732. Option C.