An ice skater is moving forward at a steady speed of 10 m/s in a straight line. Show and explain your calculation in each of the following. Assume Galilean transformations (i.e., pretend that you are solving this problem in 1904, before Einstein's papers on Special Relativity):
a) The skater tosses a coin horizontally over her shoulder straight behind her. The coin leaves her hand at 5 m/s (relative to the hand). What is the speed of the coin as viewed by a person standing still on ice?
b) the skater tosses a coin straight up (as viewed by herself), with a speed such that the coin falls back into her hand once second later. How many meters will have the coin traveled horizontally, with respect to a person standing on ice, between the moment it left the skater's hand and the moment it fell back into her hand?