Question # 1: At the Earth’s surface a projectile is launched straight up at a speed of 10.0 km/s. To what height will it rise? Ignore air resistance and the rotation of the Earth.
Question # 2: A system consists of three particles, each of mass 5.00 g, located at the corners of an equilateral triangle with sides of 30.0 cm. (a) Calculate the potential energy of the system. (b) If the particles are released simultaneously, where will they collide?
Question # 3: An object is released from rest at an altitude h above the surface of the Earth. (a) Show that its speed at a distance r from the Earth’s center, where RE < r < RE + h, is given by 
 v = sqrt(2GME (1/r - 1 ) RE + h)
Question # 4: The planet Uranus has a mass about 14 times the Earth’s mass, and its radius is equal to about 3.7 Earth radii. (a) By setting up ratios with the corresponding Earth values, find the free-fall acceleration at the cloud tops of Uranus. (b) Ignoring the rotation of the planet, find the minimum escape speed from Uranus.
Question # 5: Two spheres having masses M and 2M and radii R and 3R, respectively, are released from rest when the distance between their centers is 12R. How fast will each sphere be moving when they collide? Assume that the two spheres interact only with each other.
Question # 6: A ring of matter is a familiar structure in planetary and stellar astronomy. Examples include Saturn’s rings and a ring nebula. Consider a uniform ring of mass 2.36 x 1020 kg and radius 1.00 x 108 m. An object of mass 1000 kg is placed at a point A on the axis of the ring, 2.00 x 108 m from the center of the ring. When the object is released, the attraction of the ring makes the object move along the axis toward the center of the ring (point B). (a) Calculate the gravitational potential energy of the object-ring system when the object is as A. (b) Calculate the gravitational potential energy of the system when the object is at B. (c) Calculate the speed of the object as it passes through B.