write an article to be published in a national news paper in your country duscussing the problem facing farmers in the production of crops

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.

Carbon is allowed to diffuse through a steel plate 15 mm thick. the concentrations of carbon at the two faces are 0.65 and 0.30 kg c/m^3 fe, which are maintained constant. if the preexponential and activation energy are 6.2 x 10-7 m2 /s and 80,000 j/mol, respectively, compute the temperature at which the diffusion flux is 1.43 x 10^-9 kg/m^2 -s.

How does the electric potential energy between two charged particles change if one particle is reduced by a factor of 3? a. increased by a factor of 3 b. it is decreased by a factor of 9 c. it is reduced by a factor of 3 d. it is increased by a factor of 9