1: Determine the escape speed of a rocket on the far side of Ganymede, the largest of Jupiter's moons. The radius of Ganymede is 2.64 X 10^6m, and its mass is 1.495 X 10^23 kg. The mass of jupiter is 1.90 x 10^27 kg, and the distance between Jupiter and Ganymede is 1.071 X 10^9m. Be sure to include the gravitational effect due to jupiter, but you may ignore the motion of Jupiter and Ganymede as they revolve about their center of mass. (U = -GMm/r) 2: In 1772, the famed Italian-French mathematician Joseph Louis Lagrange was working on the infamous three-body problem when he discovered an intersting quirk in the results. If one mass is much smaller than the other two then there will exist points where this object can be stationary with respect to one of the two masses. These points are known as Lagrange points in his honor. In our treatment we could consider these points to be equilibrium points for a system. If we wanted to find Lagrange point for the Earth-Sun system located between the Earth and the Sun how far from the earth is this point and what is the significance of the other solution? The mass of the Earth is 5.98 X 10^24 kg, the mass of the Sun is 1.991 x 10^30 kg and the radius of the Earth's orbit is 1.496 x 10^11 m. (solve using quadratic eq.) 3: A climber and her gear have a combined mass of 85.0kg. If she uses a 48.0m legnth of nylon rope with a 1.00cm diameter to climb the cliff face, how much is the rope lengthened when she is at the bottom of the rope and what is the stress and strain on the rope? Now find the same things when she is halfway up the length of the rope? Neglect the mass of the rope in this problem. Young's modulus for nylon is 5.00 x 10^9 N/m^2.