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☔ Rain Umbrella Problem

Relative Velocity NEET · JEE · KCET v_rp = v_r - v_p
💧 Rain drops 🚶 Person (animated) 📐 Relative velocity vector ☔ Umbrella direction
↓ Vertically downward
→ Horizontal (east)
v_rp = v_r - v_p  |  θ = tan⁻¹(v_p / v_r)
Umbrella Angle (θ)
0.0
degrees from vertical
Relative Speed
0.00
m/s
v_rp (x-component)
0.00
m/s
v_rp (y-component)
0.00
m/s
v_r = 8.0 m/s ↓
v_p = 4.0 m/s →
v_rp = v_r - v_p = ( -4.0 , 8.0 ) m/s

☔ Umbrella should point

Forward & Vertical
Towards the relative velocity

🔍 What to Observe

  • Rain appears to come from an angle when you move
  • Umbrella angle θ = tan⁻¹(v_p / v_r)
  • Faster you walk → larger umbrella angle
  • If v_p = 0, umbrella points straight up (θ = 0°)
  • Direction changes when you turn around
Ready
θ = 0°