2. A 60 kg diver jumps off a diving board with a height of 10 meters and accelerates toward the ground. At the point shown
in the diagram, she has 1,764 Joules of gravitational energy
and 4,116 Joules of kinetic energy. What is the diver's total
mechanical energy at that point?

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.

Which object is most likely represented by a dot?

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)