Relative Velocity and Position of Ships A and B: Solving for Least Separation

AI Thread Summary
Ship A is positioned 3.3 km north and 2.7 km east of Ship B, moving south at 22 km/h, while Ship B travels at 40 km/h at a 37° angle north of east. The relative velocity of Ship A to Ship B is calculated as -31.95i - 46.07j. The position of Ship A relative to Ship B can be expressed as a function of time, but the user struggles with determining the least separation time and distance. The discussion highlights the need for guidance on solving for the least separation between the ships. Overall, the thread focuses on solving relative motion problems involving two ships with different velocities and initial positions.
Dante Tufano
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Ship A is located 3.3 km north and 2.7 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37° north of east.

(a) What is the velocity of A relative to B?

(b) Write an expression for the position of A relative to B as a function of t, where t = 0 when the ships are in the positions described as above.

(c) At what time is the separation between the ships least?

(d) What is that least separation?


2. Homework Equations : Vaw = Vab + Vbw

3. Okay, so I got the answer for part a, which is -31.95i - 46.07j, but I'm completely lost on the rest of the parts. I have no idea on how to express b in terms of i and j, let alone solve for it, any ideas?
 
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Okay, so I figured out part b, but how can I go about doing part c?
 
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