COMEDK · Physics · 4. Motion In Two Dimensions

Rain is falling vertically downwards at a velocity \(9 \mathrm{~ms}^{-1}\). And wind starts blowing at a speed of \(4 \mathrm{~ms}^{-1}\) in the west to east direction. In which direction should the girl hold her umbrella to protect herself from the rain?

A \(\theta=\tan ^{-1}(2.25)\) with the vertical towards west
B \(\theta=\tan ^{-1}(0.44)\) with the vertical towards east
C \(\theta=\tan ^{-1}(0.44)\) with the vertical towards west
D \(\theta=\tan ^{-1}(2.25)\) with the vertical towards east

Verified Solution

Answer & Solution

Correct Answer

(C) \(\theta=\tan ^{-1}(0.44)\) with the vertical towards west

Step-by-step Solution

Detailed explanation

Let the velocity of rain be \(\vec{v}_{r} = -9 \hat{j} \text{ ms}^{-1}\), where \(\hat{j}\) is the unit vector in the upward vertical direction. The velocity of the wind is \(\vec{v}_{w} = 4 \hat{i} \text{ ms}^{-1}\), where \(\hat{i}\) is the unit vector in the west to east…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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