Please help me with this review question.

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.

The solar panels used by mark function because of the photoelectric effect. light shines on the cells causing electrons to be ejected from the metal, which produces an electric current. at night on mars, no light will fall on the solar cells and no electric current will be generated. according to your notes, what type of light is typically needed to cause the photoelectric effect? a)visible b)ultraviolet c)infrared

Assume that a person skiing high in the mountains at an altitude of h = 15100 ft takes in the same volume of air with each breath as she does while walking at sea level. determine the ratio of the mass of oxygen inhaled for each breath at this high altitude compared to that at sea level. assume that the air composition (i.e. % of air that is oxygen) is the same at sea level as it is at 15100 ft.