Answer:[tex]37^{\circ}[/tex] North of west
Explanation:
Given
40,000-ton luxury line traveling 20 knots towards west and
60,000 ton freighter traveling towards North with 10 knots
suppose v is the common velocity after collision
conserving momentum in west direction
[tex]20\times 40,000=(20,000+60,000)v\cos \theta[/tex]
suppose the final velocity makes \theta angle with x axis
[tex]v\cos \theta =10----1[/tex]
Conserving Momentum in North direction
[tex]10\times 60,000=80,000\times v\sin\theta[/tex]
[tex]v\sin \theta =\frac{15}{2}----2[/tex]
divide 1 and 2
[tex]\tan \theta =\frac{3}{4}[/tex]
[tex]\theta =37^{\circ}[/tex]
so search in the area [tex]37^{\circ}[/tex] North of west to find the ship