Question

Rain drops are falling vertically down wards at 5√2m/s. A man runs horizontally in the rain at 5√2
The magnitude and direction of relative velocity of the rain drops with respect to the person is
1) 5m/s, 45° with vertical
2) 10m/s, 45° with vertical
3) 15m/s, 30° with vertical
4) none of these
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Answer 1

Answer:

option 2

Explanation:

hope gonna help you

Answer 2

Given :

Vertical velocity of the rain = 5√2 m/sec

Horizontal velocity of the rain = 5√2 m/sec

To Find :

The magnitude and direction of relative velocity of the rain drops with respect to the person

Solution :

Relative velocity is defined as the apparent velocity of a body with respect to another body that may be in motion.

Relative velocity with respect to man ($V_r$) = $\sqrt{(5\sqrt{2} )^2 + (5\sqrt{2})^2 }$

                                                                   = $\sqrt{50 + 50}$

                                                                   = $\sqrt{100}$

                                                                   = 10 m/sec

If the relative velocity makes an angle ∅ with the vertical, then

    tan∅ = $\frac{5\sqrt{2} }{5\sqrt{2} }$

⇒  tan∅ = 1

⇒       ∅ = 45°

Relative velocity makes an angle of 45° with the vertical.

Therefore, the magnitude of relative velocity of the rain drops with respect to the person is 10 m/sec and the direction of relative velocity of the rain drops is 45° to the vertical.

Hence, the correct option is (2) 10 m/sec, 45° with vertical