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Relative Motion: Rain Example

If Vr is the ...

Question

If $_{r}$ is the velocity of rain falling vertically and $_{m}$ is the velocity of a man walking on a level road, and $θ$ is the angle with vertical at which he should hold the umbrella to protect himself, then the magnitude of relative velocity of rain w.r.t man is given by

\sqrt{|_{r} |^{2} + |_{m} |^{2}}

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\sqrt{|_{r} |^{2} + |_{m} |^{2} + 2 |_{r} | |_{m} | cos θ}

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\sqrt{|_{r} |^{2} + |_{m} |^{2} - 2 |_{r} | |_{m} | cos θ}

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\sqrt{|_{r} |^{2} - |_{m} |^{2}}

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Solution

The correct option is A $\sqrt{|_{r} |^{2} + |_{m} |^{2}}$
Let the given condition be as shown in the below figure

As per the question we have
$_{r m} =_{r} -_{m}$
$\Rightarrow |_{r m} | = \sqrt{|_{r} |^{2} + |_{m} |^{2}}$

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If →Vr is the velocity of rain falling vertically and −→Vm is the velocity of a man walking on a level road, and θ is the angle with vertical at which he should hold the umbrella to protect himself, then the magnitude of relative velocity of rain w.r.t man is given by

The correct option is A √|→Vr|2+|−→Vm|2Let the given condition be as shown in the below figure As per the question we have −−→Vrm=→Vr−−→Vm ⇒ |−−→Vrm|=√|→Vr|2+|−→Vm|2

If $_{r}$ is the velocity of rain falling vertically and $_{m}$ is the velocity of a man walking on a level road, and $θ$ is the angle with vertical at which he should hold the umbrella to protect himself, then the magnitude of relative velocity of rain w.r.t man is given by

The correct option is A $\sqrt{|_{r} |^{2} + |_{m} |^{2}}$
Let the given condition be as shown in the below figure

As per the question we have
$_{r m} =_{r} -_{m}$
$\Rightarrow |_{r m} | = \sqrt{|_{r} |^{2} + |_{m} |^{2}}$