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  • A girl riding a bicycle with a speed of 5 m/s towards north direction, observes rain falling vertically down. If she increases her speed to 10 m/s, rain appears to meet her at 45^{o} to the vertical. What is the speed of the rain?

A girl riding a bicycle with a speed of 5 m/s towards the north direction, observes rain falling vertically down. If she increases her speed to 10 m/s, rain appears to meet her at 45^{o} the vertical. What is the speed of the rain? In what direction does rainfall as observed by a ground-based observer?

Answers (1)

Let the north direction be i and the south direction be j

The velocity of rain is v=a\hat{i}+b\hat{J}

Case 1 (v=5i)

The velocity of rain with respect to the girl is:

v_{r}-v_{g}=(a\hat{i}+b\hat{j})-5\hat{i}=(a-5)\hat{i}+b\hat{j}

Since the horizontal component is zero, a-5=0 \; or\; a=5

Case 2 (v=10i)

v_{r}-v_{g}=(a\hat{i}+b\hat{j})-10\hat{i}=(a-10)\hat{i}+b\hat{j}

The angle of rain appears to be 45 degrees.

\tan 45=\frac{b}{a}=\frac{b}{-5}

b=-5

So,

\left | v_{r} \right |=\sqrt{5^{2}+(-5)^{2}}=\sqrt{50}=5\sqrt{2}\; m/s

 

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infoexpert23

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