The Kentucky Derby is one of the most exciting horse races run every year. In 1973, the horse Secretariat set a record that still stands. This 500-kg horse ran the 2000-m track in 120 s. What was Secretariat's average kinetic energy? (1 kJ = 1000 J)

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.

Amoving company collects data about couches they move and displays the data in a table. the force along the ramp, the angle of the ramp, and the height the couch is raised to are shown. which statements correctly compare the work done to move the couches? check all that apply. the same amount of work is done for couches 1 and 3. the same amount of work is done for couches 2 and 3. the work for couch 1 is greater than the work for couch 2. the work for couch 2 is less than the work for couch 3. the work for couch 3 is greater than the work for couch 1. the work for couch 2 is greater than the work for couch 1.

In addition to gravity, what is the other predominant force that affects the motion of a pendulum?