If you ride on maglev train and want to shoot a duck flying in the same direction, should you aim?

Question

a) ahead of the duck,
b) right at the duck, or
c) behind the duck?

More specifically:
speed ot the train 300ft/s,
airspeed of the duck 75ft/s,
distance to the duck 500ft,
weapon is M16, muzzle velocity 3000ft/s.

-------duck--75>
.
.
.
500ft.
.
.
-------M16---------300>

Answer 1

geometry is the easiest way to do this.

assume you are traveling at 225 ft/s past a stationary duck for simplification (btw, that is one fast duck!).

obviously you need to shoot behind the duck, because your bullet will receive sideways momentum from you traveling in the train when you fire it.

the ideal would be to let a bullet fly perpendicularly just before the train draws level with the duck. you can work that out simply by saying, the bullet flies the distance across in 1/6th of a second, and therefore you should let it off 1/6th of a second before you draw level with the duck, the equivalent 225/6 = 37.5 feet behind it.

if you have to let the bullet fly as you draw level, you want to aim behind the duck at the same distance. imagine it as a vector triangle, and the angle would be arctan(37.5/500) = 4.3 degrees.

Answer 2

It takes the bullet 500/3000 = .167 seconds to travel 500 ft. Assuming you and the duck start at the same point, the train will have moved 50 feet and the duck will have moved 12.5 feet. The bullet is displaced in the direction of the motion of the train by 50 feet as well. That means you miss the duck by 37.5 ft. So you aim behind the duck and the duck "runs into" the bullet.

Answer 3

The duck flies slower than the train.

So, if you fire perpendicular to the driection of travel, the bullet will (at least initially) have a similar component of motion in the same direction as the train, as seen by a bystander.


Therefroe, if you aim at the duck that travelling in the direction of train but more slowly, by the time the bullet reaches the path of the duck, the duck will have fallen behind relative to the train (and bullet), and the bullet will whiz ahead of the duck.

Therefore, aim *behind* the duck.

Done.

Answer 4

a