A man standing on a road has to hold his umbr | vedclass

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(A) Let $\vec{v}_{r,g}$ be the velocity of rain with respect to the ground,$\vec{v}_{m,g}$ be the velocity of the man with respect to the ground,and $

Vedclass · Accepted Answer

$20 ~km/h$

Vedclass · Answer

(A) Let $\vec{v}_{r,g}$ be the velocity of rain with respect to the ground,$\vec{v}_{m,g}$ be the velocity of the man with respect to the ground,and $\vec{v}_{r,m}$ be the velocity of rain with respect to the man.When the man is at rest,the rain appears to fall at $30^{\circ}$ with the vertical,which is the direction of $\vec{v}_{r,g}$.When the man runs at $10 ~km/h$,the rain hits him vertically,meaning the horizontal component of $\vec{v}_{r,m}$ is zero.The relative velocity is given by $\vec{v}_{r,m} = \vec{v}_{r,g} - \vec{v}_{m,g}$.For $\vec{v}_{r,m}$ to be vertical,the horizontal component of $\vec{v}_{r,g}$ must be equal to the horizontal component of $\vec{v}_{m,g}$.Thus,$v_{r,g} \sin 30^{\circ} = v_{m,g} = 10 ~km/h$.$v_{r,g} = \frac{10}{\sin 30^{\circ}} = \frac{10}{0.5} = 20 ~km/h$.

$A$ man standing on a road has to hold his umbrella at $30^{\circ}$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 ~km/h$. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is:

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