A 89.5 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.57 rad/s . A monkey drops a 8.25 kg bunch of bananas vertically onto the platform. They hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 20.7 kg , drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.87 m .

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.