# Advanced projectile motion problem - moving soldier and target, both with acc.

#### evesira

Hello all,

I usually consider myself to be quite good at most things math and physics related, but compared to some of the people here, I'm sure I'm very terrible at it.

I have a very advanced projectile motion problem that I need to solve (not for school). I'm trying to contact everyone I know who might have an idea how to solve this problem.

The problem is to find the angles of fire so that a moving soldier can hit a moving target with a bullet. A full specification of the problem is in the pdf I link to below. If you can't find the exact solution, an approximate answer might also be adequate, and is desired.

As you see on the second page, the solution might require solving the moving frame of the soldier, which I don't know how to do.

Let me know if you are able to solve it, or even if you have any idea of how to approach solving it.

Thank you

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#### Feldoh

You only need one frame of reference, which will dictate everything else -- it's arbitrary what you choose as your reference frame. However there are frames of reference which make the problem easier to solve.

Mentor

#### evesira

This looks to be a repost of your thread from the end of 2008:

Is there something different? Have you made much progress on the video game yet?

I presented the problem much more clear this time, as you can see. I think people were getting confused before. The problem is exactly the same as before, yes.

And yes, i've made progress on the game. But as you can tell, I'm still hung up on this.

#### berkeman

Mentor
I presented the problem much more clear this time, as you can see. I think people were getting confused before. The problem is exactly the same as before, yes.

And yes, i've made progress on the game. But as you can tell, I'm still hung up on this.
Normally we don't allow multiple threads on the same question. But I think it may more confusing if I merge your old thread in here. I'll leave it alone for now, and hopefully you get some good replies in here.

I agree with Feldoh, and I think you should do your calculation in the frame of reference of the moving soldier. Why do you say you don't know how to do that? To get the target's velocity in the soldier's reference frame, just do a subtraction of the soldier's velocity vector (in the stationary reference frame) from the target's velocity vector (in the stationary reference frame).

#### evesira

Normally we don't allow multiple threads on the same question. But I think it may more confusing if I merge your old thread in here. I'll leave it alone for now, and hopefully you get some good replies in here.

I agree with Feldoh, and I think you should do your calculation in the frame of reference of the moving soldier. Why do you say you don't know how to do that? To get the target's velocity in the soldier's reference frame, just do a subtraction of the soldier's velocity vector (in the stationary reference frame) from the target's velocity vector (in the stationary reference frame).
Thanks.

Well I just realized that moving frame is just a fancy name for a moving coordinate system fixed on the soldier, in this case, oriented in the direction of the velocity. But now I'm not really sure how it helps to do that.

#### Feldoh

It helps to do this because now you can treat the problem as a relatively straight-forward kinematics problem. The solider is now stationary, and the target is moving with some new velocity (the original velocity of the target - the velocity of the solider) that takes the stationary solider into effect.

Once you do that you just have to find when the position of the bullet and the target meet.

"Advanced projectile motion problem - moving soldier and target, both with acc."

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