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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.

What is the mass of the water that is being heated? it requires 2,500 joules to raise a certain amount of water (c = 4.186 jig c) from 20.0°c to 60.0°c. o 159 o 40 g o 63 g o 80 g

The air in an automobile tire with a volume of 2.60 ft3 is at 70°f and 21 psig. determine the amount of air that must be added to raise the pressure to the recommended value of 30 psig. assume the atmospheric pressure to be 14.6 psia and the temperature and the volume to remain constant. the gas constant of air is ru = 53.34ft⋅lbflbm⋅r(1 psia144 lbf/ft2) = 0.3704 psia⋅ft3lbm⋅r the amount of air that must be added to raise the pressure is lbm