Classical Dynamics of Particles and Systems · Problem 10-8
Dynamics of Rigid Bodies — Marion & Thornton
Physics — Mechanics · projectile-upward-coriolis-deflection
Problem
If a particle is projected vertically upward to a height above a point on Earth's surface at a northern latitude , show that it strikes the ground at a point to the west. (Neglect air resistance, and consider only small vertical heights.)Intuitive explanation
The key is recognizing that Earth's rotation introduces a Coriolis effect that deflects moving objects. As the particle rises, it carries eastward velocity from its launch point, but the ground beneath it (at a lower latitude during ascent) moves eastward slower. When the particle falls back down, this velocity mismatch causes westward deflection relative to the ground. You'll need to track how the eastward velocity component changes with height and integrate the Coriolis acceleration over the full flight time to find the net displacement.
Intuitive explanation
The key is recognizing that Earth's rotation introduces a Coriolis effect that deflects moving objects. As the particle rises, it carries eastward velocity from its launch point, but the ground beneath it (at a lower latitude during ascent) moves eastward slower. When the particle falls back down, this velocity mismatch causes westward deflection relative to the ground. You'll need to track how the eastward velocity component changes with height and integrate the Coriolis acceleration over the full flight time to find the net displacement.