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You are in your car A on the 407 driving at a constant velocity ~vA =...

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Physics

You are in your car A on the 407 driving at a constant velocity~vA = (vA, 0, 0) and next to it another car (B) takes the exit rampon one of Toronto’s huge exchangers to get onto the 404. Forconsistency we set the two cars to start at (0, 0, 0) at t = 0 andcar B turns in the positive y direction. The exchanger can be seenas a quarter circle of radius R. 1. What are the components of thetrajectory ~rA in the reference frame of the Earth? What are thecomponents of the trajectory ~r 0 A and velocity ~v 0 A in thereference frame attached to car A? [1 mark] 2. What are thevelocity and trajectory components of car B, ~vB and ~rBrespectively, in the reference frame of the Earth? [3 marks] 3.What are the velocity and trajectory components of car B, ~v 0 Band ~r 0 B with respect to car A? [3 marks] 4. What is thecondition to see car B from car A’s window at the same position(same x component)? [1 mark] 5. Express with vB and R the durationduring which this condition holds. [2 marks]

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