Skid of weight 440 N is stuck in the middle of a circular frozen pond of radius 5 m. He cannot move because the pond is absolutely frictionless. He happens to have his 2.6 kg physics textbook so he looks for a solution to his problem. Unable to find a solution he throws his physics textbook in a fit a rage. Skid throws it at a velocity of 4 m/s directly away from him. After throwing the book, how long does it take Skid to reach the edge of the pond

A6,600 kg train car moving at +2.0 m/s bumps into and locks together with one of mass 5,400kg moving at -3.0m/s. what is their final velocity? +0.50 m/s -1.0 m/s +2.5 m/s -0.25 m/s

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 bar of prob. 5/82 is repeated here. the ends of the 0.4-m bar remain in contact with their re- spective support surfaces. end b has a velocity of 0.5 m/s and an acceleration of 0.3 m/s2 in the di- rections shown. determine the angular accelera- tion of the bar and the acceleration of end a.