Skip to content
Mechanics · Physics

Relative Velocity: Rain and River Simulation

Walk through the rain and cross a river to see velocities add as vectors, from the ground and from a moving frame. Find the umbrella angle, the quickest crossing and the way to land directly opposite.

Interactive virtual lab · no download · works on phones and laptops

Chapter
Motion in a Plane
For
Class 11 · JEE · NEET
Time
~12 min

How to use it

  1. 1Rain: set the walking speed, rain speed and wind.
  2. 2Switch to the man's frame to see the rain slant.
  3. 3River: set width, current, swimmer speed and heading.
  4. 4Use Least time, Land opposite and Least drift.

What to notice

  • Rain relative to a walker comes from in front at tan α = v_man/v_rain.
  • Heading straight across gives the least time, w/u, whatever the current.
  • To land opposite, aim upstream at sin θ = v_river/v_swimmer.
  • If the river is faster than the swimmer, landing opposite is impossible.

For teachers

Teach it in 20 minutes

A lesson plan, questions to put to the class, a quick quiz you can project or print, and the formulas behind Relative Velocity: Rain and River.

  1. 1Hook

    ~2 min
    • Ask: “It's raining straight down and you start walking. Why do you tilt your umbrella forward?” Then switch to the walker's frame.

  2. 2Demonstrate

    ~7 min
    • Rain: set the walking speed, rain speed and wind.
    • Switch to the man's frame to see the rain slant.
    • River: set width, current, swimmer speed and heading.
    • Use Least time, Land opposite and Least drift.

  3. 3Pause and ask

    ~5 min
    • Have a student say this in their own words: Rain relative to a walker comes from in front at tan α = v_man/v_rain.
    • Have a student say this in their own words: Heading straight across gives the least time, w/u, whatever the current.
    • Have a student say this in their own words: To land opposite, aim upstream at sin θ = v_river/v_swimmer.
    • Have a student say this in their own words: If the river is faster than the swimmer, landing opposite is impossible.

  4. 4Check

    ~6 min
    • Run the 6-question quiz below: project it and take answers by show of fingers (1–4), or print it as a worksheet.

About the Relative Velocity: Rain and River simulation

Velocity depends on who is watching. Rain falling straight down looks slanted to someone walking, because relative to them it also has their velocity reversed. A swimmer in a river moves with the water and through it at the same time: the velocity over the ground is the vector sum of the two. These are the two classic relative-velocity problems of Class 11 kinematics.

In this relative velocity simulation you walk through rain (with or without wind), switch between the ground's view and the walker's view, and tilt an umbrella to stay dry. Then you cross a river: set its width and current, your swimming speed and heading, and compare the quickest crossing with the one that lands directly opposite.

Also covers: rain man problem, umbrella angle, river crossing, boat river problem, shortest time, shortest path, drift.

Frequently asked questions

At what angle should a man hold his umbrella in the rain?

Along the rain's velocity relative to him: tilted forward by α where tan α = (his speed)/(rain's speed) when the rain falls vertically.

How should a swimmer head to cross a river in the least time?

Straight across. Only the across-component of the velocity relative to the water decides the time, and it is largest when all of it points across.

How can a swimmer reach the point directly opposite?

By heading upstream at sin θ = v_river/v_swimmer, so the upstream component cancels the current. This is impossible if the river flows faster than the swimmer swims.

What is the least drift when the river is faster than the swimmer?

Head upstream at sin θ = u/v; the drift is then w√(v² − u²)/u.

Try next

All simulations