Projectile Problem: Aim 10 Meters Above Target?

[Gamerex]

My physics instructor and I were arguing about this today. It was a problem involving ranges, but the fundamental issue is this:

If you aim a projectile at a target, and the projectile passes 10 meters below the target, do you aim 10 meters above the target to compensate?

 

[jedishrfu]

I would say no. It's perhaps a useful approximation. The reason is ideal flight of a projectile is a parabola. You'd be shooting from the same spot both times. If you were to plot both trajectories out there may be one spot where the difference is 10m but not at all spots.

The real case is more complicated with air resistance blunting the parabolic flight causing the projectile to drop more quickly toward end of the flight. Again there's probably one spot where your 10m difference holds but not at all spots.

Wikipedia has an article on "range of a projectile"

 

[sophiecentaur]

That method of compensation will work to some extent but it depends upon the details of the trajectory. If the projectile dips 10m over a 50m range, aiming 10m high will not do the job. Over a km, the method will give a much better result. Compensating in this way relies on assuming that the flight time is the same for both elevations (and, hence, the amount of drop). In fact, it never is the same but the error is less for a less curved, flatter, trajectory (as with the high velocity 1km example).