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

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 ramp on one of Toronto’s huge exchangers to get onto the 404. For consistency we set the two cars to start at (0, 0, 0) at t = 0 and car B turns in the positive y direction. The exchanger can be seen as a quarter circle of radius R. 1. What are the components of the trajectory ~rA in the reference frame of the Earth? What are the components of the trajectory ~r 0 A and velocity ~v 0 A in the reference frame attached to car A? [1 mark] 2. What are the velocity and trajectory components of car B, ~vB and ~rB respectively, in the reference frame of the Earth? [3 marks] 3. What are the velocity and trajectory components of car B, ~v 0 B and ~r 0 B with respect to car A? [3 marks] 4. What is the condition 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 duration during which this condition holds. [2 marks]

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genius_generous answered 2 years ago

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