What physical laws or relationships can be applied or derived in a given system involving projectile motion, including the parabolic path of a projectile?

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.

Aparticle moves in the xy plane with constant acceleration. at time zero, the particle is at x = 6 m, y = 8.5 m, and has velocity ~vo = (9 m/s) ˆı + (−2.5 m/s) ˆ . the acceleration is given by ~a = (4.5 m/s 2 ) ˆı + (3 m/s 2 ) ˆ . what is the x component of velocity after 3.5 s? answer in units of m/s.

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".