55 points question
please put the answer in order by up to down
please help me

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

For this car, predict the shape of a graph that shows distance (x) versus time (t). note that time is the independent variable and will be on the bottom axis. need asap

Why is the energy that results from a roller coaster's position at the top of a hill referred to as potential energy?