Which of the following cycles tracks the movement of the hydrosphere? a. the rock cycle b. the hydrogen cycle c. the water cycle d. the nitrogen cycle

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.

Assume that a person skiing high in the mountains at an altitude of h = 15100 ft takes in the same volume of air with each breath as she does while walking at sea level. determine the ratio of the mass of oxygen inhaled for each breath at this high altitude compared to that at sea level. assume that the air composition (i.e. % of air that is oxygen) is the same at sea level as it is at 15100 ft.

This is a form of winter precipitation. it is frozen precipitation falling as ice pellets. snowflakes melt into raindrops as they pass through a thin layer of warmer air. the raindrops then refreeze into particles of ice when they fall into a layer of sub-freezing air near the surface of the earth. this precipitation is called a) hail. b) rain. c) sleet. d) snow.