Answer to Question #99677 in Mechanics | Relativity for nurul

Question #99677
Consider an air-borne humanitarian mission, where food packages where dropped
with zero initial speed, from a helicopter hovering a height of h above the Earth
surface. Treating the package as particle of mass m, derive the horizontal deflection
from the particle caused by the Coriolis force acting on a particle falling freely in Earth’s
gravity field.
1
Expert's answer
2019-12-02T09:53:34-0500

The Coriolis force is much smaller in magnitude that the force of gravity.

In this case, Ώ is a small parameter.

We can writer

z=hg×t×t2(1)z=h-\frac {g×t×t}{2} (1)

The particle hits the ground when

t=2hg(2)t=\sqrt {\frac {2h}{g}} (2)

The net eastward deflection of the particle as strikes the ground is

d=Ωˊ3×cosλ×8×h×h×hgd=\frac {Ώ}{3} × \cosλ×\frac {8×h×h×h}{g}



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