Question

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(from my calculus book when I was a student!) Two highways intersect at right angles. From out point of view, Car A on one highway is 0.5 km from the intersection and is moving toward it at 96 km/hr, while car B on the other highway is 1 km from the intersection and is moving away from it at 88 km/hr. We would therefore call the position and velocity of car A to us to be Position: XA to us-(0.5 km) Velocity: VA to us km 36- hr 96 km/hc 0.5 km 88 kmh L.0 km METHOD 1: using straight calculus (A) Using your favorite techniques of related rates , determine the rate that the distance between the two cars is changing at this instant. METHOD 2: using vectors Let's do this problem from B's viewpoint (riding in the car with B) (B) Determine the velocity (in component and polar form) of car A from B's point of view (C) Determine the "line of sight" of car A from car B by computing XA to us-Ag to us in (D) On the diagram, draw in both the vectors determined from parts (B) and (C) with the tails (E) Using the line of sight as your "horizontal axis", break the velocity of the car vector into by computing the VA to us VB to us component and polar form. placed at car A's location. a right triangle with one leg parallel to the line of sight and the other leg perpendicular to the line of sight. (F) Compute the component of the velocity vector along the line of sight.

Answer 1

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