Coriolis Effect on Fast Projectile

In summary, the projectile fired at high velocity v_0 toward the east will be deflected by the Coriolis effect in the direction of south. The formula for the deflection can be determined by using the angular velocity \omega of the earth, the latitude \lambda where the projectile is fired, and the distance traveled D, which is \omega D^2 \sin\lambda / v_0. However, the question's use of "nearly horizontally" may have actually meant "nearly vertically" and this would affect the accuracy of the formula.
  • #1
e(ho0n3
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A projectile is fired nearly horizontally at high velocity [itex]v_0[/itex] toward the east. (a) In what direction is it deflected by the Coriolis effect? (b) Determine a formula for the deflection is terms of [itex]v_0[/itex], the angular velocity [itex]\omega[/itex] of the earth, the latitude [itex]\lambda[/itex] where the projectile is fired, and the distance traveled D.

I don't know why the problem says "nearly horizontal" instead of just horizontal. Since the projectile is traveling pretty fast, I guess I can ignore the effects of gravity.

Now, suppose I shoot somebody located directly east of me (how evil!). Since the Earth is round, the shot will be gaining height with respect to the ground directly below it right? Now, from the shooter's perspective, this is also happening right? So the shot is moving upward. Now I haven't made any use of the Coriolis effect so my latter explanation is probably bogus. Now, [itex]\vec{a}_C = -2\vec{\omega} \times \vec{v}_0[/itex]. Using the right hand rule, it seems that the Coriolis acceleration [itex]\vec{a}_C[/itex] is pointing away from the Earth which seems to support my first idea. Now, the books answer is South for some unknown reason so I don't know what to think anymore. Any help here?
 
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  • #2
I think the question meant to say "nearly vertically". The verticality would be affected by the Coriolis acceleration making it impossible to be exactly vertical.

Yes, if you threw horizontally, there would not be a southward migration. Unless it's winter and you're throwing birds.
 
  • #3
Gokul43201 said:
I think the question meant to say "nearly vertically". The verticality would be affected by the Coriolis acceleration making it impossible to be exactly vertical.
But how do you throw "nearly vertically" to the east. That makes no sense unless I'm throwing at an angle to the horizontal. I'll post the answer to (b) in hopes of any enlightment.

Answer (b): [itex]\omega D^2 \sin\lambda / v_0[/itex]
 

1. What is the Coriolis Effect?

The Coriolis Effect is a phenomenon that occurs due to the rotation of the Earth. It causes objects, such as projectiles, to appear to curve to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

2. How does the Coriolis Effect affect fast projectiles?

The Coriolis Effect affects fast projectiles by causing them to deviate from their intended path. This is because the Earth's rotation causes the projectile's trajectory to appear to curve, resulting in a change in direction.

3. Does the Coriolis Effect have a greater impact on faster projectiles?

Yes, the Coriolis Effect has a greater impact on faster projectiles because they cover a larger distance in a shorter amount of time, allowing for the rotation of the Earth to have a greater effect on their trajectory.

4. How does the Coriolis Effect impact long-range shots?

The Coriolis Effect can have a significant impact on long-range shots, especially at high latitudes. The further the distance a projectile travels, the more time it has to be affected by the Earth's rotation, resulting in a greater deviation from the intended target.

5. Can the Coriolis Effect be accounted for in projectile trajectory calculations?

Yes, the Coriolis Effect can be accounted for in projectile trajectory calculations by taking into consideration the projectile's speed, the Earth's rotation rate, and the latitude of the launch site. This allows for more accurate predictions of the projectile's path and helps compensate for the impact of the Coriolis Effect.

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