The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below: car a y = 60x + 10 car b y = 40x + 70 after how many hours will the two cars be at the same distance from their starting point and what will that distance be?

Write short note on the following ; collision theory, rotation angle and angular velocity, centripetal acceleration, coriolis force, and newton's law of gravitation.

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.

You have a pick-up truck that weighed 4,000 pounds when it was new. you are modifying it to increase its ground clearance. when you are finished