Question

A particle of mass 3 units moves in xy plane under influence of a force field having potential V equal to 12x(3y-4x).The particle starts at time t=0 from rest and the point with position vector 10i-10j. 1.set up differential equations and conditions describing the motion 2.solve the equations in (1) 3.find the position at any time 4.Find the velocity at any time

Answer 1

We are given the potential of the field = $12x(3y-4x)$

field = $\frac{∂V}{∂x}i+\frac{∂V}{∂y}j+\frac{∂V}{∂z}z$ =$(36y-96x)i+36xj$

here the field will be equal to the acceleration

as we can see that the components of the field are interdependent on each other