An athlete completes 4 laps around a track with a radius of 25 meters in 12 minutes(720 seconds). What is tye magnitude of the athlete's tangential velocity? Hint: to answer correctly, "time" must be solved for 1 lap and the SI unit for velocity is (m/s).

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.

In a system, when potential energy decreases, then entropy also decreases. true false

What is the role of lenses in microscopy?