Calculate the relativistic energy e and momentum p of a proton of mass m = 1 gev/c^2 moving at velocity u = 0.9c in the laboratory frame. then calculate the " in-variant, mass" k^2-e^2-p^2c^2 in the laboratory frame. compare your result to the invariant mass k'^2 in the frame where the proton is at rest (v'=0) what do you conclude?

Afisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. it takes a time of 2.20 s for the boat to travel from its highest point to its lowest, a total distance of 0.670 m . the fisherman sees that the wave crests are spaced a horizontal distance of 5.80 m apart. (a) how much is the wavelength? (b) find the period of the wave. (c) how fast are the waves traveling? (d) what is the amplitude a of each wave?