Rain falls vertically at 10 m/s. A person walks north at 10 m/s. The umbrella should be tilted at what angle with the vertical?

Solution

Physics sir · 3 steps

Find the rain relative to you: subtract your velocity, and the rain seems to come from the front.

1. Relative velocity. The umbrella must face the rain as you see it. That is v⃗ᵣₘ = v⃗ᵣ - v⃗ₘ: the rain's velocity minus your own.
2. Two components. The rain has 10 m s⁻¹ downward. Subtracting your 10 m s⁻¹ north adds 10 m s⁻¹ toward the south. So the rain seems to come down and toward you from the front.

   tan θ = vₘ/vᵣ = 10/10 = 1

3. So. θ = 45° with the vertical, with the umbrella tilted forward toward the north. The answer is (b).

The idea to keep. In rain-man problems, always find rain relative to the man. Tilt the umbrella against that relative velocity, at tan θ = vₘₐₙ/vᵣₐᵢₙ from the vertical.

Answer from the NTA final answer key. Solution by PrepWiser.