$m$ at $\overset { \rightarrow }{ r } ={ r }_{ 0 }\hat { i }$.

We have placed a particle of massAt $t=0$ 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