You research your favorite topic: earthquakes. You build a tall LEGO building, and you want to know which type of motion is most damaging to your building. You discover in your research that side-to-side motion is the worst. You will place the building on a piece of wood and shake it for durations of 30 seconds, 60 seconds, and 90 seconds. You will try an up-and-down motion and side-to-side motion.

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.

Light traveling in water, nwater = 1.33, strikes a plastic block at an angle of incidence of 51.4°; part of the beam is reflected and part is refracted. if the index of refraction of the plastic is 2.0, what is the angle made by the reflected and refracted beams?

The energy equivalent of the rest mass of an electron is