Question

A boy running on a horizontal road at 8km/h finds rain falling vertically. He increases his speed to 12km/h and finds the drops make 30^∘ with the vertical. The speed of rain with respect to the road is:

• A. \( 4\sqrt{7}\,\text{km/h} \)
• B. \( 9\sqrt{7}\,\text{km/h} \)
• C. \( 12\sqrt{7}\,\text{km/h} \)
• D. 15√(7)km/h

Hint:

Relative velocity problems often use triangle geometry.

Answer 1

The Correct Option is A

Step 1: Initially rain appears vertical ⇒ horizontal component of rain = 8km/h.
Step 2: When speed becomes 12km/h: tan 30^∘ = (12 - 8)/(v) ⟹ v = 4√(3)
Step 3: Resultant speed: vᵣ = √(4√(3))² + 8² = 4√(7)km/h