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If \( \mathrm{Vr} \) is the velocity of rain falling vertically and \( \mathrm{Vm} \) is the velocity of a man walking on a level road, and \( \theta \) is the angle with vertical at which he should hold the umbrella to protect himself, than the relative velocity of rain w.r.t. the man is given by:
(a) \( \mathrm{Vrm}=\sqrt{\mathrm{Vr}^{2}+\mathrm{Vm}^{2}+2 \mathrm{VrVm} \cos \theta} \)
(b) \( \mathrm{Vrm}=\sqrt{\mathrm{Vr}^{2}+\mathrm{Vm}^{2}-2 \mathrm{VrVm} \cos \theta} \)
(c) \( \mathrm{Vrm}=\sqrt{\mathrm{Vr}^{2}+\mathrm{Vm}^{2}} \)
(d) \( \mathrm{Vrm}=\sqrt{\mathrm{Vr}^{2}-\mathrm{Vm}^{2}} \)
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