Relative velocity and distance between particles

AI Thread Summary
To determine the shortest distance between two particles A and B, first establish the distance as a function of time based on their velocities and initial positions. The cosine rule can be applied if the angle between the particles is known, specifically if it is 90 degrees. Next, calculate the first derivative of the distance function to identify the time at which this distance is minimized. Finally, substitute this time back into the distance function to find the minimum distance. This approach effectively utilizes calculus and trigonometry to solve the problem.
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Homework Statement



Lengths L₁, L₂. Velocities V₁, V₂.

Homework Equations



Find the shortest distance between particle A and B.

The Attempt at a Solution



[I seriously don't have any clue how to start this question itself.
 

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You sholud first find the distance between the two given objects as a function of time. I'm not sure if \theta in your picture is 90^{\circ} angle or not, but cosine rule will definitely work.

Then you find the first derivative of that function in order to find the time at which the distance is minimum. When you got that time, it's easy to find the distance by plugging it back to the distance function.
 

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