Attraction is not the sure way for testing polarity. explain

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.

Awave is produced in a rope. the wave has a speed of 33 m/s and a frequency of 22 hz. what wavelength is produced?

Imagine you are standing in the antarctic during the southern hemisphere summer. the sky is clear and blue. there are no clouds in the sky. your shadow is cast on the icy ground. what is the color of the shadow?