A girl standing on road holds her umbrella at 45 ° with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15 √(2) kmh ⁻¹, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is: (a) 30 kmh ⁻¹ (b) (25)/(√(2)) kmh ⁻¹ (c) (30)/(√(2)) kmh ⁻¹ (d) 25 kmh ⁻¹

Answer: (c). Umbrella at 45°: rain's horizontal and vertical components are equal, vx = vy. Running at 15√(2) makes rain vertical, so vx = 15√(2) ⇒ vy = 15√(2) km/h. Relative to the girl only vy remains: 15√(2) = (30)/(√(2)) km h⁻¹ So the answer is (c).

A girl standing on road holds her umbrella at 45 ° with the vertical… | JEE Main 2022 (27 Jun, Shift 1)

Q10JEE Main 2022 · 27 JUN · SHIFT 1Medium

Relative Velocity in Two Dimensions

A girl standing on road holds her umbrella at 45 $^\circ$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15 $\sqrt{2}$ kmh ${}^{-1}$ , the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is:

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Answer: (c)

Umbrella at $45^\circ$ : rain's horizontal and vertical components are equal, $v_x = v_y$ .
Running at $15\sqrt{2}$ makes rain vertical, so $v_x = 15\sqrt{2} \Rightarrow v_y = 15\sqrt{2}\text{ km/h}$ .
Relative to the girl only $v_y$ remains: $15\sqrt{2} = \frac{30}{\sqrt{2}}\text{ km h}^{-1}$
So the answer is (c).

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