An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 31.7 years in the space-ship's frame of reference. Assume the galaxy is 2.00 million light years away and his speed is constant. Required:
a. How fast must he travel relative to Earth?
b. What will be the kinetic energy of his spacecraft, which has a mass of 1.00 x 10^6 kg?
c. What is teh cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0 cents per kWh?

convex lenses are thicker at the middle. rays of light that pass through the lens are brought closer together (they converge). a convex lens is a converging lens. when parallel rays of light pass through a convex lens the refracted rays converge at one point called the principal focus.

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jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.