The Maple Leafs are playing the Habs (Go Habs Go!), and they are stuck in their zone. They decide to ice the puck, and John Tavares starts from one end of the rink at a constant speed of 5m/s. Carey Price is 3m in front of him, but gets hooked by the traitor John Tavares, so Price must start from rest. If Price’s acceleration is 0.77/ 2 , a) How long is it before Tavares overtakes him? b) Who gets to the puck first at the other end of the 60m long rink? c) How far apart are the players at that time, and how fast are they moving? What does this imply?

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.

Acup of coffee sits on the dashboard of an automobile. the car goes around a sharp curve. even though you hold the cup still, coffee still splashes out. this can best be explained due to a) density. b) friction. c) gravity. d) inertia.

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].