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Question: If \(\overset{\rightarrow}{r}\) = bt<sup>2</sup>\(\widehat{i}\) + ct<sup>3</sup>\(\widehat{j}\), whe...

If r→\overset{\rightarrow}{r} = bt2i^\widehat{i} + ct3j^\widehat{j}, where b and c are positive constant, the time at which velocity vector makes an angle q = 60º with positive y-axis is –

A

cb\frac{c}{b}

B

2b33c\frac{2b}{3\sqrt{3}c}

C

2c3b\frac{2c}{\sqrt{3}b}

D

2b3c\frac{2b}{\sqrt{3}c}

Answer

2b33c\frac{2b}{3\sqrt{3}c}

Explanation

Solution

dr→dt\frac{\overset{\rightarrow}{dr}}{dt} = 2bt i^\widehat{i} + 3ct2 j^\widehat{j}

tan 60060^{0} = 2bt3ct2\frac{2bt}{3ct^{2}}

̃ t = 2b33c\frac{2b}{3\sqrt{3}c}