Problem Set 2

# Problem Set 2 - 1 Physics 200a PSII 1. Let A = 3i + 4j and...

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1 Physics 200a PSII 1. Let A = 3 i + 4 j and B = 5 i - 6 j . (i) Find A + B , A - B , 2 A +3 B , and C such that A + B + C = 0 . (ii) Find A , the length of A and the angle it makes with the x-axis. 2. A train is moving with velocity v TG = 3 i + 4 j relative to the ground. A bullet is ﬁred in the train with velocity v BT = 15 i - 6 j relative to the train. What is the bullets’ velocity v BG relative to the ground? 3. Consider the primed axis rotated relative to the unprimed by an angle φ in the counterclockwise direction. (i) Derive the relation A x = A 0 x cos φ - A 0 y sin φ A y = A 0 y cos φ + A 0 y sin φ that expresses unprimed components in terms of primed compo- nents of a vector ~ A using class notes if needed to get started. (ii) Invert these relations to express the primed components in terms of unprimed components. In doing this remember that the sines and cosines are constants and that we should treat A 0 x and A 0 y as unknowns written in terms of knowns A x and A y . (Thus multiply one equation by something, another by something else, add

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## This note was uploaded on 07/13/2008 for the course PHYS 200 taught by Professor Ramamurtishankar during the Fall '08 term at Yale.

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Problem Set 2 - 1 Physics 200a PSII 1. Let A = 3i + 4j and...

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