# Solve for trajectory (if you can)

We have placed a particle of mass $$m$$ at $$\overset { \rightarrow }{ r } ={ r }_{ 0 }\hat { i }$$.

At $$t=0$$ we have given it a velocity of $$\overrightarrow { v } ={ v }_{ 0 }\hat { j }$$.In the whole co-ordinate plane the force is given by $$\overrightarrow{F}=\frac { -8 }{ { r }^{ 3 } } \overrightarrow { r }N$$

The title says solve for trajectory but I am telling you that the trajectory of the particle is ellipse.If the eccentricity of the ellipse is given by $$e=\frac { a }{ b }$$ where $$a,b$$ are co-prime integers then find $$a\times b$$

Details and Assumptions:

1)$${ v }_{ 0 }=1m/s,{ r }_{ 0 }=2metre,m=1Kg$$

2)There are no other force acting on the particle except the force given.

3) Ignore gravity

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