Question

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.

Answer 1

Answer:$37^{\circ}$ 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

$20\times 40,000=(20,000+60,000)v\cos \theta$

suppose the final velocity makes \theta angle with x axis

$v\cos \theta =10----1$

Conserving Momentum in North direction

$10\times 60,000=80,000\times v\sin\theta$

$v\sin \theta =\frac{15}{2}----2$

divide 1 and 2

$\tan \theta =\frac{3}{4}$

$\theta =37^{\circ}$

so search in the area $37^{\circ}$ North of west to find the ship