Please help me solve this physics question. Please provide all necessary step to

Question

Please help me solve this physics question. Please provide all necessary step to step details with a diagram appropriate to the 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 50,000-ton cruise ship, the Hangover, it was going due west at a speed of 20 knots in calm seas through the fog just before it was struck broadside by the 70,000-ton ore 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. Your answer must be organized, clear, and complete. See the mastery problem rubric for a reminder of what should be included for a perfect score.

Explanation / Answer

given,

mass of first ship = 50000 tons or 45359237 kg

mass of second ship = 70000 tons or 63502932 kg

initial velocity of first ship = 20 knots or 10.2889 m/s toward west

initial velocity of second ship = 10 knots or 5.14444 m/s toward north

by conservation of momentum

initial momentum = final momentum

momentum = mass * velocity

for east-west direction

45359237 * 10.2889 = (45359237 + 63502932) * vx

vx = 4.287 m/s

for north south direction

63502932 * 5.14444 = (45359237 + 63502932) * vy

vy = 3 m/s

final velocity = sqrt(vx^2 + vy^2)

final velocity = sqrt(4.287^2 + 3^2)

final velocity after collision = 5.232 m/s or 10.170194 knots

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