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Rain and umbrella problem
Intermediate
Rain appears to fall at an angle depending on your own velocity.
The rain's velocity relative to you is v_rain − v_you. If you walk, the rain seems to slant toward you at angle tanθ = v_you/v_rain from the vertical, so tilt the umbrella forward.
Rain at 4 m/s vertically, you at 3 m/s: relative rain speed 5 m/s, tilt 37° forward.
The tilt depends on your speed, not the direction you face.
In more detail
To find how rain appears to fall to a moving person, subtract the person's velocity from the rain's velocity. The result shows the direction the person should tilt the umbrella.
Real-world uses
- Walkers hold umbrellas at an angle to shield against rain falling at a slant.
- Rain-gauge design takes wind into account when collecting rainfall.
- Walking in the rain, you feel the drops hitting you at a slant even when they fall vertically, because your own motion changes their apparent direction.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why does rain look slanted when I walk?
Because the rain's velocity relative to you includes your forward motion, which makes it appear to come from ahead.
Which way should I tilt the umbrella?
Tilt it so that it points along the direction of the relative velocity of the rain.
Why do I need to tilt the umbrella forward when I walk?
The rain seems to come at you at an angle set by your walking speed, so you tilt the umbrella forward to block the drops.
Related topics in Kinematics
Effect of air resistance · Relative velocity in 2D · River-boat problems · Uniform circular motion · Angular displacement and velocity · Period and frequency