Answer to Question #99677 in Mechanics | Relativity for nurul

Question

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.

Answer 1

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

In this case, Ώ is a small parameter.

We can writer

$z=h-\frac {g×t×t}{2} (1)$

The particle hits the ground when

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

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

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