If r⃗ = bt2i^+ct3j^, where b and c are positive constants, when does the velocity vector make an angle of 45.0∘ with the x - and y-axes?

Question

Chemistry

Yadira

3 July, 00:18

If r⃗ = bt2i^+ct3j^, where b and c are positive constants, when does the velocity vector make an angle of 45.0∘ with the x - and y-axes?

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Answers (1)

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Alisson Pearson · Answer 1

The displacement function is given by : r = bt2i + ct3j meters

The velocity function is the derivative of the displacement:

v = r' = 2bti + 3ct2j meter / second

Now, for the velocity vector make an angle of 45.0∘ with the x - and y-axes, the i and j components have to be equal:

2bt = 3ct2 (Now solve for t)

2bt = t (3ct)

either t = zero (rejected)

or t = 2b / 3c seconds (accepted)