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Coriollis Force and Noninertial Frames

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A particle is projected vertically upward from the surface of the earth at colatitude (polar angle) theta.

It rises to a height (h << R_earth) and then falls back to the surface. Show that it strikes the ground at a distance (8/3)*omega*sin(theta)*Sqrt(2h^3/g) to the west of the initial position, where omega = angular velocity of the earth's rotation, and g - gravitational acceleration. What is its westward displacement at its maximum height?

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Solution Summary

The westward displacement at a particle's maximum height is calculated.

Solution Preview

Please see the attachments for the solution.

In the rotating frame the particle's velocity is:

The projection of earth's rotation on in the rotating frame is:

So the Coriollis' acceleration is:

Hence, in the ...

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