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The velocity of rain with respect to ground is

Asked by Prashant DIGHE | 13 Jul, 2019, 10:09: AM

Expert Answer

velocity of man with respect to ground

begin mathsize 14px style u with rightwards arrow on top space equals space u i with hat on top end style

...............(1)

Let velocity of rain with respect to ground,

begin mathsize 14px style v with rightwards arrow on top space equals space a space i with hat on top space plus space b space j with hat on top end style

...............(2)

relative velocity of rain with respect to man,

begin mathsize 14px style v with rightwards arrow on top space minus space u with rightwards arrow on top space equals space left parenthesis a minus u right parenthesis i with hat on top space plus space b space j with hat on top end style

................(3)

since the rain appears falling vertical, we have (a-u) = 0 in eqn.(3), hence a = u

relative velocity of rain with respect to man when he doubles the speed ,

begin mathsize 14px style v with rightwards arrow on top space minus space 2 u with rightwards arrow on top space equals space left parenthesis u minus 2 u right parenthesis i with hat on top space plus space b space j with hat on top space equals space minus u space i with hat on top space plus space b space j with hat on top end style

................(4)

if the rain appears falling in a line that makes an angle θ with vertical, then we have ,

tanθ = b/-u or b = -u tanθ

hence velocity of rain with respect to ground,

begin mathsize 14px style v with rightwards arrow on top space equals space u space i with hat on top space minus space left parenthesis u space tan theta right parenthesis space j with hat on top end style

Answered by Thiyagarajan K | 13 Jul, 2019, 02:50: PM

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