NASA is conducting a test with the Perseverance Rover to investigate the gravity on Mars. They test a pendulum with a length of L on the Earth and find it has a period of 1.0s. The Perseverance Rover has a similar pendulum with a length of L/2. If the acceleration due to gravity on Mars is 1/3 the acceleration due to gravity on the Earth, what is the period of the Perseverance Rover's pendulum on Mars? A .82 s
B .67 s
C 1.50 s
D 1.22 s

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.