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JEE MainPhysicsMotion in Two Dimensions

A person walking on a horizontal road at a speed of 3 3 km h ⁻¹ observes the rain falling exactly vertically. When the person stops, the rain appears to fall at an angle of 30^ with the vertical. The actual speed of the rain drops with respect to the ground is

Options

  1. A6 3 km h ⁻¹
  2. B9 km h ⁻¹
  3. C6 km h ⁻¹
  4. D3 3 km h ⁻¹

Correct answer

A. 6 3 km h ⁻¹

Step-by-step solution

Let the actual velocity of the rain be v _r = v_x i - v_y j . When the person is moving with velocity v _p = 3 3 i , the relative velocity of the rain is v _ rp = (v_x - 3 3 ) i - v_y j . Since the rain appears to fall exactly vertically to the moving person, the horizontal component of the relative velocity must be zero. Therefore, v_x = 3 3 km h ⁻¹ . When the person stops, the rain appears to fall at an angle of 30^ with the vertical. This gives the direction of the actual velocity of the rain: (30^ ) = v_x v_y 1

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