1. The problem statement, all variables and given/known data (i) A particle of mass m moves in the x - y plane. Its coordinates are x(t) and y(t). What is the kinetic energy of this particle? (ii) The potential energy of this particle is V (y). The actual form of V will remain unspecied, except that it depends only on the y coordinate. Write down the Lagrangian for this particle. Obtain the equation of motion. (iii) Apart from the energy, what other physical quantity is conserved, and why? 2. Relevant equations N/a 3. The attempt at a solution[/b Ok so I'm new to Lagrangian, anyway from what i understand would the kinetic energy just be? T(v)=1/2mv^2 ; where v = ydot, but i dont understand whether it is y dependant or x dependant, would it be y dependant because the potential energy given in part 2 is y dependant so they act in same plane? In part 2, L(y,v) = T(y,v)-V(y,v) ; where v=ydot, so after using the lagrangians equation d(mv)/dt=ydot since y is not specified? and for part 3 im taking a complete guess at momentum because F=ydot=dp/dt. No idea very stuck =/ if someone could explain would be much appreciated thanks.