B Air Gun Sighted at a Falling Target Demonstration

[mopit_011]

So in class today, we were talking about how if you fire a bullet aimed at a falling target and release the target and the bullet at the exact same time, they will surely collide. I asked if air resistance (since it’s not a constant force) wouldn’t affect the collision and my teacher didn’t have a response. Could I have help please?

 

[BvU]

Hi,

​

Good question !

Without air resistance the bullet trajectory is a parabola (the black line in the picture here ) .
That is what your exercises will want for your near future.

With air resistance the bullet slows down considerably and follows a (much) more complicated trajectory.
The target will also experience air resistance, but most likely not in the exact same way as the bullet (feather target? brick target?).
It would be somewhat coincidental if both drop equally far over the distance of the shot.

$\$

 

[hutchphd]

If the drag force of the air has no vertical component (only affecting the horizontal velocity component) the target will still be intercepted although the juncture may change.
Typically the drag force is antiparallel to the velocity itself and so the result may be affected. Obviously for the classroom demo these effects are small enough to ignore (because most of the drag is in fact horizontal).
Your Prof probably didn't want to wander off into the weeds ! But you know intuitively that a very highly viscous fluid will ruin the result. Depending on your level of skill you could refine this question...like how much does air drag affect the result etc etc. Good question.

 

[berkeman]

So in class today, we were talking about how if you fire a bullet aimed at a falling target and release the target and the bullet at the exact same time, they will surely collide. I asked if air resistance (since it’s not a constant force) wouldn’t affect the collision and my teacher didn’t have a response. Could I have help please?

As already mentioned, air resistance will slow the bullet and the velocity of the falling object, but because the velocity profiles of each of those is different, it becomes a more complicated problem.

But for short-range monkey falling problems, the monkey does not do so well...

 

[A.T.]

I asked if air resistance (since it’s not a constant force) wouldn’t affect the collision ...

In general, it will. Imagine the target hangs on a parachute (not uncommon in war).