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Question

The position vector of a moving particle in xy plane can be represented as r=(2tˆi+2t2ˆj)m, where t represents the time instant. The rate of change of θ at time t=2s. (where θ is the angle which its velocity vector makes with positive xaxis)

A
25 rad/s
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B
217 rad/s
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C
2 rad/s
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D
4 rad/s
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Solution

The correct option is B 217 rad/s
Here the position vector is shown in the diagram below

x=2tvx=dxdt=2y=2t2vy=dydt=4t
tan(θ)=vyvx=4t2=2t
Diffrentiating with respect to time we get,
(sec2θ)dθdt=2
or (1+tan2(θ))dθdt=2, or (1+4t2)dθdt=2
dθdt=21+4(2)2=217 rad/s

For detailed solution watch the next video.


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