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Question

A girl riding a bicycle with a speed of 5 ms1 towards north direction, observes rain falling vertically down. If she increases her speed to 10 ms1, rain appears to meet her at 45 to the vertical. What is the speed of the rain?

A
5 2 ms1
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B
5 ms1
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C
10 2 ms1
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D
10 ms1
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Solution

The correct option is A 5 2 ms1

Let us assume north is in ^i direction and vertically downwards is ^j direction

Let the velocity of rain vr=a^i+b^j
Given, Velocity of girl, vg=5^i

Velocity of rain w.r.t girl, vrg=(a5)^i+b^j
According to question, rain appears to fall downwards
Hence, a5=0a=5

Given, velocity of girl increased to , vg=10^i m/s

Velocity of rain appears to fall to the girl, vrg=vrvg=(a10)^i+b^j
Now the rain appears to fall at 45o
Hence , b=a10b=5

Velocity of rain, vr=5^i5 hatj

Speed of rain, |vr|=52+52=52 m/s

1504634_938699_ans_c07d64cee5c94a268a32a35607727f4e.PNG

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