Somebody i’m desperate, i’ll give brainliest!

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.

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

Electric field of the earth. the earth has a net electric charge that causes a field at points near its surface equal to 150 n> c and directed in toward the center of the earth. (a) what magnitude and sign of charge would a 60-kg human have to acquire to overcome his or her weight by the force exerted by the earth’s electric field? (b) what would be the force of repulsion between two people each with the charge calculated in part (a) and separated by a distance of 100 m? is use of the earth’s electric field a feasible means of flight? why or why not?