A man is running on a level road with a speed | vedclass

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Question

(C) Let the velocity of the man be $\vec{V}_m = 10 \hat{i} \ m/s$.The velocity of the rain relative to the man is $\vec{V}_{rm} = -10 \sqrt{3} \hat{j}

Vedclass · Accepted Answer

$10 \sqrt{7} \ m/s$

Vedclass · Answer

(C) Let the velocity of the man be $\vec{V}_m = 10 \hat{i} \ m/s$.The velocity of the rain relative to the man is $\vec{V}_{rm} = -10 \sqrt{3} \hat{j} \ m/s$.The velocity of the rain $\vec{V}_r$ is given by $\vec{V}_{rm} = \vec{V}_r - \vec{V}_m$,so $\vec{V}_r = \vec{V}_{rm} + \vec{V}_m = 10 \hat{i} - 10 \sqrt{3} \hat{j} \ m/s$.Now,the man runs in the opposite direction,so his new velocity is $\vec{V}_{m'} = -10 \hat{i} \ m/s$.The new relative velocity of the rain with respect to the man is $\vec{V}_{rm'} = \vec{V}_r - \vec{V}_{m'} = (10 \hat{i} - 10 \sqrt{3} \hat{j}) - (-10 \hat{i}) = 20 \hat{i} - 10 \sqrt{3} \hat{j} \ m/s$.The magnitude of this relative velocity is $|\vec{V}_{rm'}| = \sqrt{(20)^2 + (-10 \sqrt{3})^2} = \sqrt{400 + 300} = \sqrt{700} = 10 \sqrt{7} \ m/s$.

$A$ man is running on a level road with a speed of $10 \ m/s$. He feels that the rain is falling vertically downward with a speed of $10 \sqrt{3} \ m/s$. If he runs in the opposite direction with the same speed,then the speed of the rain relative to him will be:

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