Imagine a tall building located on the Earth’s equator. As the Earth rotates about its own axis, 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 person on the ground is closer to the Earth’s axis. Consequently, if an object is dropped from the top floor to the ground a distance, h =97.2m below, it lands east of the point vertically below where it was dropped. How far (in centimeters) to the east will the object land? Hint: Earth completes a rotation about its axis in 24 hours. Express your answer in terms of h, g = 9.81 m/s2, and the linear speed, v(in terms of angular speed) of the Earth first, before number-crunching. Ignore air resistance and assume free-fall acceleration is constant over the fall.
Imagine a tall building located on the Earth’s equator. As the Earth rotates about its own axis, 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 person on the ground is closer to the Earth’s axis. Consequently, if an object is dropped from the top floor to the ground a distance, h =97.2m below, it lands east of the point vertically below where it was dropped. How far (in centimeters) to the east will the object land?
Hint: Earth completes a rotation about its axis in 24 hours. Express your answer in terms of h, g = 9.81 m/s2, and the linear speed, v(in terms of angular speed) of the Earth first, before number-crunching. Ignore air resistance and assume free-fall acceleration is constant over the fall.
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