A spaceship's orbital maneuver requires a speed increase of 1.30 x 10° m/s. If its engine has an exhaust speed of 2.15 x 10° m/s, determine the required ratio 2 of its initial mass to its final mass. (The difference M, - M equals the mass of the ejected fuel.)

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 kg and is approaching at 8.5 m/s due south. The second car has a mass of 550 kg and is approaching at 15 m/s due west. (a) Calculate the magnitude of the final velocity, in meters per second, of the cars. (b) Calculate the direction of the final velocity, in degrees south of west, of the cars. (c) What is the change in kinetic energy, in joules, for the collision? (This energy goes into the deformation of the cars.)

A spaceship's orbital maneuver requires a speed increase of 1.05 ✕ 103 m/s. If its engine has an exhaust speed of 2.45 ✕ 103 m/s, determine the required ratio  Mi Mf  of its initial mass to its final mass. (The difference  Mi − Mf  equals the mass of the ejected fuel.)