A steamer is moving towards east with a velocity u.
A second steamer is moving a velocity 2u at angle `theta` north of east. The motion of the second steamer relative to the first is along north- east . Show that, `cos theta-sin theta =1/2`

Explanation

Let us choose,x -axis along east and y-axis along north. Then the velocities are of first steamer, `vecv_(1) =uhati`, of second steamer, `vecv_(2)= 2ucos theta hati+2usin theta hatj`
`therefore` Velocity of the second steamer relative to the first is,
`vecw =vecv_(2)-vecv_(1)=u(2cos theta-1)hati+2usinthetahatj`
As `vecw` is along north -east , its x-and y-components are equal.
`therefore u(2 cos theta-1)=2usin theta or, 2 cos theta-2sin theta =1 or, cos theta -sin theta =1/2`.