Does technology always follow science

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.

What is the magnitude of the gravitational force acting on the earth due to the sun?

The two metal spheres in the figure are connected by a metal wire with w switch in the middle. initially the switch is open. sphere 1, with the larger radius, i'd given a positive charge. sphere 2, with the smaller radius, is neutral. then the switch is closed. afterward, sphere 1 has charge q1, is at potential v1 and the electric field strength at its surface is e1. the values for sphere 2 are q2, v2, and e2. a. is v1 < ,> , or = to v2? explain. b. is q2 < , > , or = explain? c. is e1 < ,> ,or = to e2? explain?