Ball 1, with a mass of 20kg, is moving to the right at 20m/s. at what velocity should ball 2, with a mass of 40kg, move so that they both come to a stand still upon collision?

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.

By what primary heat transfer mechanism does the sun warm the earth?

Aswimming pool whose volume is 10 comma 000 gal contains water that is 0.01% chlorine. starting at tequals0, city water containing 0.003% chlorine is pumped into the pool at a rate of 5 gal/min. the pool water flows out at the same rate. what is the percentage of chlorine in the pool after 1 hour? when will the pool water be 0.006% chlorine?