As part of an interview for a summer job with the Coast Guard, you are asked to help determine the search area for two sunken ships by calculating their velocity just after they collided. According to the last radio transmission from the 40,000-ton luxury liner, the Hedonist, it was going due west at a speed of 20 knots in calm seas through a rare fog just before it was struck broadside by the 60,000- ton freighter, the Ironhorse, which was traveling north at 10 knots. The transmission also noted that when the freighter's bow pierced the hull of the liner, the two ships stuck together and sank together. To determine the search area find the resulting components of the velocity.

The resultant velocity is  

Explanation:

Apply the law of conservation of momentum

Where is the mass of the Luxury Liner = 40,000 ton

            is the velocity of Luxury Liner = 20 knots due west

            mass of freighter = 60,000

            is the velocity of freighter = 10 knots due north

Apply the law of conservation of momentum toward the the west direction

So the equation would be

Substituting values

Where the final velocity due west

Making the subject

Apply the law of conservation of momentum toward the the north direction          

So the equation would be

Where the final velocity due north

     Making the subject

The resultant velocity is

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle