Express fx and fy in terms of the length of the vector f and the angle θ in paired form

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.

The diagram shows a series of volcanic island and a hot spot determine the direction of movement of the tectonic plate that for the island

Gasoline comes from petroleum, which is made from ancient living things. petroleum, therefore, contains a type of energy. a. heat b. nuclear c. biological d. chemical potential