Question

A man running at 8kmph feels rain drops vertical. He increases his speed to 12kmph, rain drops strikes

him at the angle of 30° with vertical. Find velocity of rain..​

Answer 1

Explanation:

Let the rain drops have a velocity of v kmph and be inclined at an angle A wrt the vertical. So they make an angle 90-A wrt the road.

horizontal component of rain drops = v cosA = 8 kmph. --- (1)

When the person speeds up to 12 kmph, then rain drops fall at an angle of 30 deg. in the opposite direction. Net horizontal component of relative velocity = 12 kmph - 8 kmph = 4 kmph

so tan 30 = 4/(v sin A) => v sin A = 4 √3 kmph ---(2)

so v^2 = 112 => v = 4 √7 kmph

Angle that rain makes with the road

= 90-A = cos⁻¹ (2/√7) = 40.89 deg.

hope it helps u ✌