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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.

Suppose an objects initial velocity is 10m/s and it’s final velocity is 4 m/s. mass is constant. what can best be concluded about the object based in the work-energy theorem

An alien spaceship is 500 m above the ground and moving at a constant velocity of 150 m/s upwards. how high above the ground is the ship after 5 seconds?