2. Assume the height of the roller coaster (see fig) is y = 40 m (take the reference point, y = 0, as the bottom of the coaster hill). If the car starts from rest at point A, what is the speed of the car at the bottom of the hill? 3. What is the speed of the car when it reaches point B?

PICTURE IS BELOW ATTACHED

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 discovery of the electron as a subatomic particle was a result of

The energy equivalent of the rest mass of an electron is