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Name: Stephen
Status: student
Grade: 9-12
Location: NJ
Country: N/A
Date: 4/18/2005


Question:
If a projectile is fired from the Northern Hemisphere at x-degrees-N a target at the same longitude in the Southern Hemisphere at x-degrees-S, then the Coriolis Effect work the same as it would if the target was also in the Northern Hemisphere. I asked my teacher if this conjecture was true and she did not know. Is my conjecture true (maybe because the Earth always rotates in the same direction)?


Replies:
Yes, you are absolutely right! (If I understand you correctly) A point at x degrees south latitude moves east at the same speed as a point at x degrees north latitude. Therefore, if a projectile is fired due south from a point at x degrees north latitude and lands at x degrees south latitude, it will land at the same longitude as it was launched at. If, on the other hand, it has half the range and lands at 0 degrees latitude (at the equator), it will land west of the longitude it was launched at since the equator is travelling east at a speed greater than any other point on the earth's surface.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University


I am going to ignore air resistance. I do not understand the question, so I am just going to tell you what would happen.

On the way from the firing point to the equator, the bullet would apparently veer to the west, because its initial eastward speed (the speed at which the firing position is moving east) will not change as it travels, and this is less than the eastward speed of the ground at any point between the firing position and the equator. From the equator on south, the bullet's eastward speed is still less than the eastward speed of the ground under it (though the difference decreases as it moves further south) so it will continue to veer west. It will stop veering west when it reaches the latitude x S, but it will miss the target no matter what else it does.

The amount by which it will miss the target depends on its southward speed: the faster it is going, the smaller the distance by which it will miss. Actually, its southward speed is not a free variable. If it is really intended to hit the target, its southward speed must be such that it neither flies off into space nor falls to the ground. This means its speed satisfies v^2/r = 9.8 m/s^2, where r is the radius of Earth. In other words, it must be in orbit.

Tim Mooney



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