Question

To a person walking at 2 kmph rain appears to fall vertically. When he doubles his speed ran appears to fall at 300 to vertical. The actual velocity of rain is

Answer 1

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

Let velocity of rain vr=ai^+bj^

speed of rain=a2+b2−−−−−−√

Case I:

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

vrm=v¯r−v¯m

vm=3i^

vrm=(a−3)i^+bj^

Since vrm is vertical

a−3=0=>a=3

Case II:

when relative velocity is at 45∘

v¯m=6i^

vrm=(a−6)i^+bj^

=−3i^+bj^

Since tanθ=b−3

tan 45=1

=> |b|=3

Therefore Speed=32+32−−−−−−√=32–√

Hence d is the correct answer.