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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.

Which safety measures should you follow during a thunderstorm? check all that apply. (a) avoid touching anything that conducts electricity. (b) avoid touching a person who has been struck by lightning. (c) go outside. (d) keep your computer turned off. (e) stay out of water. (f) stay inside.

Which configuration would produce an electric current? a) rotate a coil of copper wire between two magnets. b) connect a wire between a copper and zinc strip sitting in a beaker of water. c) connect a wire to the (+) positive end of a battery and the other end to a light bulb. d) connect a wire to the negative end of a battery and the other end to a light bulb.