To a man walking at a rate of 3km/hr the rain appeares to fall vertically when he increases his spee

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Blazing goIITian

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Let Velocity of rain, V_R= V₁i + V₂j

Velocity of person firstly, V_P1=3i

Velocity of person secondly,V_P2=6i

Velocity of rain w..t Person firstly,V_R/P1=V_R - V_P1

=( V₁-3) i + V₂ j

Since rain is falling vertically V₁- 3 =0 => V₁ = 3

Velocity of rain w.r.t person secondly ,V_R/P2 = V_R - V _P2

=(V₁-6) i +V₂ j

Since rain appears to fall at 45⁰ with the vertical, tan 45⁰ =(V₁ - 6)/V₂

=> V₂ = -3

So, V_R =3i -3j

Magnitude of V_R =(3² + 3²)^1/2 =3

and direction 45⁰ along clockwise direction.

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