Please Help! WILL GIVE BRAINLIEST IF ANSEWR IS CORRECT!!!
(See picture for question.)

How much work would be needed to raise the payload from the surface of the moon (i.e., x = r) to an altitude of 5r miles above the surface of the moon (i.e., x = 6r)?

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.

According to newtons universal law of gravitation, which would change the parh of the ball so it traces out widest curved path possible?