A bullet of mass 0.05 kg travels at a speed of 400 m/s toward a 1 kg block at rest on a frictionless surface and becomes imbedded in it. It is attached to a wall by a spring with a 38,000 N/m spring constant. What is the velocity of the block just after impact and what is the maximum compression of the spring. How much kinetic energy is lost during the impact

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.