Coriolis Force and westward deflection of a falling object
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A) A projectile is fired straight up at a speed of v0 at a latitude of (alpha) degrees. Show
that in the time the projectile is airborne, it is deflected a distance of 4 v0*3 cos(alpha)/3 g^2 to the west.
c) Show that for objects confined to land or for objects in which their net vertical acceleration is small in the inertial reference frame, such as storm systems, the maximum magnitude of the Coriolis force is at the north pole with a maximum magnitude of 2m* (Omega0)* v0, where v0 is the object's speed in the east-north direction, or another words along the ground. Thus, show even for fast moving objects with speeds of say 100 m/s, the ratio of the Coriolis acceleration=to that of g is approximately 0.15 percent.
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Absolutely clear and step by step solution is provide to two problems involving Coriolis force. If you are struggling to visualize or understand the concept of Coriolis force this problem set is ideal for you. It will provide you the necessary understanding and problem solving skills in Coriolis Forces.
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a) A projectile is fired straight up at a speed of v0 at a latitude of (alpha) degrees. Show
that in the time the projectile is airborne, it is deflected a distance of 4 v0*3 cos(alpha)/3 g^2 to the west.
At the altitude of α, choose the coordinates axes as shown in the diagram. x axis towards east (in to the paper in the 2 D picture above), y axis is towards north and z is perpendicular to the surface of the earth at that location.
We need to write the components of the angular velocity vector and the velocity of the projectile in this coordinate system.
w = (0, cos α, sin α)
v = (0, 0, vo - gt)
Note that at any time t after projection, z component of the velocity is obtained by using
v = u + at è v = vo - gt
F = - 2m (w x v) = ...
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