82 CHAPTER 2. LINEAR TRANSFORMATIONS

50. An illustration used in many beginning physics books is that of firing a rifle hori-zontally and dropping an identical bullet from the same height above the perfectlyflat ground followed by an assertion that the two bullets will hit the ground at ex-actly the same time. Is this true on the rotating earth assuming the experimenttakes place over a large perfectly flat field so the curvature of the earth is not anissue? Explain. What other irregularities will occur? Recall the Coriolis accelerationis 2ω [(−y′ cosϕ) i+(x′ cosϕ+ z′ sinϕ) j− (y′ sinϕ)k] where k points away from thecenter of the earth, j points East, and i points South.