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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 km h⁻¹, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is

Asked in JEE Main 27th June 1st Shift 2022 · Relative velocity of two moving bodies

Answer: (3) (30)/(√2) km h⁻¹

Step-by-step solution

Standing: the rain comes at 45° to the vertical, so its horizontal and vertical components are equal, vₓ = v_y.

Running at 15√2 km/h the rain appears vertical, so vₓ = 15√2 km/h and hence v_y = 15√2 km/h.

Relative to the running girl only the vertical part remains: 15√2 = (30)/(√2) km/h.

Why the other options are wrong

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