The rain is falling vertically with a speed $4 m s^{- 1}$ and a man is moving due east with a speed $3 m s^{- 1}$ . With what speed does the rain appear to be falling (for the man)? Also at what angle should he hold the umbrella to protect himself from rain?

5 m s^{- 1}, 37^{\circ} with respect to vertical

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5 m s^{- 1}, 53^{\circ} with respect to vertical

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5 m s^{- 1}, 45^{\circ} with respect to horizontal

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5 m s^{- 1}, 30^{\circ} with respect to horizontal

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Solution

The correct option is A $5 m s^{- 1}, 37^{\circ} with respect to vertical$
The given situation can be shown as

We have from the question
${\to v}_{r m} =_{r} -_{m} = - 4^j - 3^i$
$\Rightarrow |_{r m} | = 5 m s^{- 1}$
and $θ = {tan}^{- 1} (\frac{3}{4}) = 37^{\circ}$
with respect to vertical.

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The rain is falling vertically with a speed 4 ms−1 and a man is moving due east with a speed 3 ms−1. With what speed does the rain appear to be falling (for the man)? Also at what angle should he hold the umbrella to protect himself from rain?

The correct option is A 5 ms−1,37∘ with respect to vertical The given situation can be shown as We have from the question →vrm=→vr−−→vm=−4^j−3^i ⇒ |−−→vrm|=5 ms−1 and θ=tan−1(34)=37∘ with respect to vertical.

The rain is falling vertically with a speed $4 m s^{- 1}$ and a man is moving due east with a speed $3 m s^{- 1}$ . With what speed does the rain appear to be falling (for the man)? Also at what angle should he hold the umbrella to protect himself from rain?

The correct option is A $5 m s^{- 1}, 37^{\circ} with respect to vertical$
The given situation can be shown as

We have from the question
${\to v}_{r m} =_{r} -_{m} = - 4^j - 3^i$
$\Rightarrow |_{r m} | = 5 m s^{- 1}$
and $θ = {tan}^{- 1} (\frac{3}{4}) = 37^{\circ}$
with respect to vertical.