Consider a tall building located on the Earth’s equator. As the Earth rotates, a person on the top floor of the building moves faster than someone on the ground with respect to an inertial reference frame, because the latter person is closer to the Earth’s axis. Consequently, if an object is dropped from the top floor to the ground a distance h below, it lands east of the point vertically below where it was dropped.
(a) How far to the east will the object land? Express your answer in terms of h, g, and the angular speed ώ of the Earth. Neglect air resistance, and assume that the free-fall acceleration is constant over this range of heights. (b) Evaluate the eastward displacement for h = 50.0 m.
(c) In your judgment, were we justified in ignoring this aspect of the Coriolis effect in our previous study of free fall?