Question

A man walking in rain at a speed of 3kmph find rain to be falling verticall

Answer 1

Answer

Let i^i^ and j^j^ be unit vector in horizontal and vertical respectively.

Let velocity of rain vr=ai^+bj^vr=ai^+bj^

speed of rain=a2+b2−−−−−−√=a2+b2

Case I:

when relative velocity of rain w.r.t man is vertical

vrm=v¯r−v¯mvrm=v¯r−v¯m

vm=3i^vm=3i^

vrm=(a−3)i^+bj^vrm=(a−3)i^+bj^

Since vrmvrm is vertical

a−3=0=>a=3a−3=0=>a=3

Case II:

when relative velocity is at 45∘45∘

v¯m=6i^v¯m=6i^

vrm=(a−6)i^+bj^vrm=(a−6)i^+bj^

=−3i^+bj^=−3i^+bj^

Since tanθ=b−3tan⁡θ=b−3

tan 45=1

=> |b|=3|b|=3

Therefore Speed=32+32−−−−−−√=32–√Speed=32+32=32

Hence d is the correct answer.
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