Describe the particle motion diagram for two runners during a race in which the first runner crosses the finish line as the other runner is three-fourths of the way to the finish line.

What is work? how much work is done to move an object 0 meters?

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.

1. a net force of 100 newton’s is applied to a wagon for 5 seconds. this causes the wagon to undergo a change in momentum of