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A bullet of mass m is fired with muzzle speed v 0 horizontally and due north from a position at colatitude 8°. Find the direction and magnitude of the Coriolis force iN terms of m, v 0, 8°, and the Earth's angular velocity Ω. How does the Coriolis force compare with the bullet's weight if v0


a) Exceeds the weight.

b) Is equal to the weight.

c) Is less than the weight.

d) Cannot be determined from the information provided.

1 Answer

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Final answer:

The Coriolis force acting on a bullet fired northward at a colatitude of 8° will be to the right (eastward) with a magnitude based on the Earth's angular velocity and the bullet's muzzle speed. The Coriolis force is typically much smaller than the bullet's weight.

Step-by-step explanation:

The Coriolis force is an apparent force that arises from the Earth's rotation and affects the motion of objects moving over the surface of the Earth. For a bullet of mass m fired northward with a muzzle speed v0 at a colatitude of 8°, the direction of the Coriolis force would be to the right (eastward) in the northern hemisphere. The magnitude of the Coriolis force, Fc, can be given by the expression Fc = 2mv0Ω sin(θ), where θ is the colatitude (90° - latitude) and Ω is the Earth's angular velocity.

To compare the Coriolis force with the bullet's weight, we need to look at the ratio of the muzzle speed v0 to the weight of the bullet. In the cases where v0 exceeds, equals, or is less than the weight, the magnitude of the Coriolis force would change proportionally. However, because the Coriolis force is usually much smaller than forces resulting from Earth's gravity, in most practical scenarios involving bullets, the Coriolis force would be significantly smaller than the bullet's weight.

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