Rain, driven by the wind, falls on a railway compartment with a velocity of `20 ms^-1`, at an angle of `30^@` to the vertical. The train moves, along the direction of wind flow, at a speed of `108 km h^-1`. Determine the apparent velocity of rain for a person sitting in the train.

Options

A. `20 sqrt(7) ms^-1`
B. `10 sqrt(7) ms^-1`
C. `15 sqrt(7) ms^-1`
D. `10 sqrt(7) km h^-1`

Answer

B

Explanation

(b) Speed of train `= 108 xx (5)/(18) = 30 ms^-1`
Let `vec V_R and vec V_T` represent the respective velocities of rain and train.
Now, the relative velocity of rain w.r.t. person (train) is given by `v_(R,T) = vec v_R - vec v_T rArr vec v_r + (-vec v_T)`
Let `vec(O R) and vec(R T)` represent the vectors, respctively, in magnitude and direction.
`O T^2 = OR^2 + RT^2 + 2 OR. RT cos 120^@`
=`20^2 + 30^2 - 2 xx 20 xx 30 xx (1)/(2)`
=`400 + 900 - 600 = 700 = sqrt(700) ms^-1`
=`10 sqrt(7) ms^-1.
.