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 ?

1 Answer
Oct 4, 2017

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