Relative Velocity — Rain on a Moving Window
Rain falls dead straight down, yet it streaks backwards across the window of a moving train. Switch between the ground and the rider to watch the relative-velocity rule being built piece by piece: observed minus observer.
Como usar esta simulação
- Press Ground frame and Rider's frame to switch the observer and watch the slant appear
- Set the rain speed and the train speed independently to change the apparent angle
- Load the metro example at 5.0 m/s with rain at 30°, or the 45° train exercise
- Try Two cars meeting at right angles for a case with no vertical motion at all
O que observar
- The rain is vertical from the ground and slanted from the train, at the same instant
- A faster train slants the rain further back without changing how fast it falls
- The apparent angle is set by the ratio of the two speeds, not by either alone
- Reversing which object is the observer reverses the relative velocity exactly
- For the two cars at right angles the relative speed exceeds either car's own speed
A física por trás
A velocity is only meaningful once a frame is named. The velocity of B as seen by A is v_AB = v_B − v_A, the observed velocity minus the observer's. Rain falling vertically at v_r has no horizontal component in the ground frame; in the frame of a train moving at v_t the rain acquires a horizontal component of −v_t, so it appears to slant backwards at an angle given by tan θ = v_t/v_r. Nothing about the rain has changed — only the frame it is described in.