Arock with a mass of 2.0 kg falls from a cliff. at a height of 5.0 meters, its velocity is 6.0 m/s. what is the mechanical energy of the rock?

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.

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

Infrared rays have a shorter wavelength than question 11 options: x-rays. ultraviolet rays. radio waves. gamma rays.