Urgent Help with these questions

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.

Click the game tab at the bottom of the simulation and select level 1. (there is no seesaw balance for this part of the activity.) balance the first equation, and click check to see if you got it right. if you can’t balance it in the first try, you can try again. work through the five equations for level 1. click continue to go on to level 2, and later level 3. each level is more difficult than the one before. keep trying until all the equations are balanced. in one or two sentences, describe how you did in the balancing game. in a few more sentences, explain one strategy you learned for balancing more complex equations.

Which model displays the change in a gas when the temperature of the gaseous system decreases?