To a man running upwards on the hill, the rain appears to fall vertically downwards with `4 m s^-1`. The velocity vector of the man w.r.t. earth is `(2 hat i + 3 hat j) ms ^-1`. If the man starts running down the hill with the same speed, then determine the relative speed of the rain w.r.t. man.
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Explanation

Velocity of rain w.r.t. man, `vec v_(r,m) = vec v_r - vec v_m`
`-4 hat j = 2 hat i - hat j`
When man starts running down,
`vec v'_(r,m) =vec v_r - vec v_m = 2 hat i - hat j + 2 hat i + 3 hat j = 4 hat i + 2 hat j`
Speed `=|vec v_(r,m)| = sqrt(16 + 4) = sqrt(20) ms^-1`.