Two rocks collide in outer space. Before the collision, one rock had mass 9 kg and velocity < 4700, -3100, 2300> m/s. The other rock had mass 5 kg and velocity < -400, 2200, 3600> m/s. A 3 kg chunk of the first rock breaks off and sticks to the second rock. After the collision the 6 kg rock has velocity < 1800, 650, 1500> m/s. After the collision, what is the velocity of the other rock, whose mass is now 8 kg

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 car has the most kinetic energy? a. a car of mass 1000 kg with a speed of 3 m/s b. a car of mass 2000 kg with speed 7 m/s c. a car of mass 1000 kg with speed 7 m/s d. a car of mass 2000 kg with speed 3 m/s

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.)