A roller coaster with a mass of 500.0 kg starts from a height of 27.0 meters with a speed of 5.6 m/s. It descends to a height of 2.00 meters before it starts back up. Some energy is loss to the work due to friction. The speed at the bottom of the ramp is 22.0 m/s. How much energy was lost to friction?

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.