Part A) What is the distance between the two ships two hours after they depart?

Question

Part A) What is the distance between the two ships two hours after they depart? Express your answer with the appropriate units. Part A) What is the distance between the two ships two hours after they depart? Express your answer with the appropriate units. Part B) What is the speed of ship A as seen by ship B? Express your answer with the appropriate units.

Secure | https://session.masteringphysics.com/myct/iter K Ch 04 Problem 4.61 Ships A and B leave port together. For the next two hours, ship A travels at 30.0 mph in a direction 50.0° west of north while the ship B travels 50.0 east of north at 30.0 mph

Explanation / Answer

Part A -

First of all, split the velocity into x and y components:

Ship A velocity = (30 cos(50+90), 30 sin(50+90))
Ship B velocity = (30 cos(-50+90), 30 sin(-50+90))

So, after 2 hours:

ship A position = (60 cos(140),60 sin(140))
ship B position = (60 cos(40), 60 sin(40))

Distance = sqrt((60 cos(140) - 60 cos(40))^2 + (60 sin(140) - 60 sin(40))^2))
= sqrt((-46 - 46)^2 + (38.6 - 38.6)^2))

= sqrt(8464 + 0) = 92.0 mile

Part B -

difference in speed = (30 cos(140) - 30 cos(40), 30 sin(140) - 30 sin(40))

speed of ship A as seen by ship B = sqrt((30 cos(140) - 30 cos(40))^2 + (30 sin(140) - 30 sin(40))^2))
= sqrt((-23 - 23)^2 + (19.3 - 19.3)^2)

= 46 mile per hour.

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