Auroras are frequently seen
a. near the equator.
b. after solar flares.
c. before a sunspot cycle.
d. every 11 years.

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.

How does the kinetic energy of a charge change as the charge moves under the effect of an electric field from higher potential to lower potential? a. the kinetic energy increases. b.the kinetic energy decreases. c.the kinetic energy remains the same. d.the kinetic energy is always zero.

Light traveling in a medium with a refractive index 1.19 is incident on a plate of another medium with index of refraction 1.79. at what angle of incidence is the reflected light fully polarized?