2 Points
When must scientific theories be changed?

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 frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.

Apulley with mass mp and a radius rp is attached to the ceiling, in a gravity field of 9.81 m/s2 and rotates with no friction about its pivot.