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A particle move in x-y plane such that i...

A particle move in `x-y` plane such that its position vector varies with time as `vec r=(2 sin 3t)hat j+2 (1-cos 3 t) hat j`. Find the equation of the trajectory of the particle.

Text Solution

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Comparing `vec r=(2 sin 3t)hat j+ 2(1-cos 3t) hat j`
With `vec r =xhat I + hat j`, we have `x =2 sin `3t` and `y =2(1-cost)`.
This gives `sin3t=(x)/(2)` and `cos 3t =1-(y)/(2)`.
Eliminating `t` by squaring and adding the above terms, we have
`(x^(2)/(4)+(1-(y^(2))/(2))=1`.
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