Question

A butterfly is flying with velocity `10 i +12 j m/s` and wind is blowing along x axis y with velocity u. If butterfly starts motion from A and after some time reaches point B, What is the value of u ?

Answer 1

`vec(u)=((x_B-x_A)/t-10)i+((y_B-y_A)/t-12)j`
(see below for definition of variables)

Explanation:

Assuming
`i` is the unit vector in the positive `x` direction;
`j` is the unit vector in the positive `y` direction;
point A has coordinates (in meters) `(x_A,y_A)`; and
point B has coordinates (in meters) `(x_B,y_B)`
then

The displacement from point A due to flight
after some period of time `t` sec. would be
`(10i+12j)(m/sec) xx t sec = (10i+12j)t (m)`

The displacement due to the wind after `t` sec. with a velocity of `vec(u)(m/sec)` parallel to the X-axis would be
`vec(u) * t (m)`

The total displacement from A to B would be
`(10i+12j+vec(u))t (meters)`

In terms of the points `A:(X_A,y_A)` and `B:(x_B,y_B)`
and using the unit vectors `i` and `j`
this displacement is
`(x_B-x_A)i+(y_B-y_A)j (meters)`

Therefore
`(10i+12j+vec(u))t=(x_B-x_A)i+(y_B-y_A)j`

and
`vec(u)=((x_B-x_A)/t-10)i+((y_B-y_A)/t-12)j`