When Zulu arrived late at the lecture hall, the professor was saying, “you can add them together in two different ways: one way results in nothing, the other results in twice as much.” What was the professor talking about?

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.

5400 j of energy are given off when a 50 g of aluminum pan changes temperature. does the temperature of the pan increase or decrease and by how much?

How to know which equation of motion to use where?explain