6. A rocket is fired vertically upwards from rest and burns fuel at a constant rate k, and the exhaust gases are ejected vertically downwards with constant speed u relative to the rocket. The initial mass of the rocket is M', half of which is fuel. During the time that the fuel is being burned, air resistance may be neglected and the Earth’s gravitational field may be assumed to give rise to an acceleration of constant magnitude g, where ku >M'g. Show that the speed of the rocket when the fuel runs out is given by uln2-gM'/2k, and find the distance traveled at this time. 2.According to Einstein’s theory of special relativity, the kinetic energy K of a mass m moving at velocity v is given by K=[(mc^2)/(1-(v/c)^2)^0.5]-mc^2 Show that at v<<c, the kinetic energy of the mass reduced to the Newtonian expression. 5. (10 marks) Two identical particles of mass m attract each other with a force that obeys Newton’s third law. They are initially at rest on a smooth inclined plane which has an angle of inclination of 45 degrees w.r.t. the horizontal. Find the acceleration of the center of mass of the system. how to solve them? thanks!