A police officer is driving due north at a constant speed of 23 m/s relative to

Question

A police officer is driving due north at a constant speed of 23 m/s relative to the ground when she notices a truck on the east-west highway ahead of her, driving west at a high speed. She finds that the truck's speed relative to her car is 44 m/s (about 98 mph). (a) Sketch the vector triangle that shows how the truck's velocity relative to the ground is related to the police car's velocity relative to the ground and to the truck's velocity relative to the police car. The sketch need not to be to scale, but the velocity vectors should be oriented correctly and bear the appropriate labels.

Explanation / Answer

R = V_police + V_truck

44{1,0} = 23{0,1} + V_truck

V_truck = {44,-23}

|V_truck| = 49.65 m/s

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