A man moving with `5 ms^-1` observes rain falling vertically at the rate of `10 m s^-1`. Find the speed and direction of the rain with respect to ground.

Explanation

`vec v_(r,m) = -10 hat j ms^-1, vec v_m = 5 hat i m s^-1`
`vec v_(r,m) = vec v_r - vec v_m`
`vec v_r = vec v_(r,m) + vec v_m = (-10 hat j) + (5 hat i) m s^-1`
`rArr |vec v_r| = 5 sqrt(5) m s^-1`
Inclination of the rain with vertical, `tan theta = (1)/(2)`
`rArr theta = tan^-1 (1)/(2)`.
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