Can a Bomb Hit the Plane Below?

[hogrampage]

Homework Statement

Two bombers are flying 100m apart at the same speed. One is directly below the other. If the bomber above releases its bomb, will it hit the bomber below it?

Homework Equations

y - y_o = -1/2gt²
x = v_ot

The Attempt at a Solution

I set the initial velocity to something like 55 m/s and solved for t in the first equation, then solved the x distance using t. I found t to be 4.52s and x to be 248.46m (if my calculations were correct). I don't know how to determine if the bomb will hit the plane below the upper plane using this information.

 

[kuruman]

I set the initial velocity to something like 55 m/s and solved for t in the first equation, then solved the x distance using t. I found t to be 4.52s and x to be 248.46m (if my calculations were correct). I don't know how to determine if the bomb will hit the plane below the upper plane using this information.

You solved for t how? What does that t = 4.52 s represent? The time needed for what to do what?

 

[JaredJames]

Does the question not give you any dimensions? Speed of the aircraft?

OK, I'm going to try this:

You know the bombs initial velocity is 0m/s = u, the acceleration is 9.8m/s^2 = a and the distance it travels is 100m = s (for the purpose of this you are interested in how fast it travels that distance).

So with v^2 = u^2 + 2as, you can input your values and come out with a final velocity (v). This tells you how fast the bomb is traveling downwards (at the 100m mark, after which is irrelevant to the question). Once you have v, you can use this with v = u + at to rearrange and get time (t). You now know how long it took to drop.

Now the key here is that this only covers the vertical component. You would also have to calculate the horizontal component, which you can't do without the bombers speed.

Once you have both of them, you can then see whether or not the bombs trajectory will intercept the lower bomber. You may even have to look at the lower bombers length, just because the point directly below will be clear, doesn't mean the tail will (or the nose depending how it comes out).

Not sure if I can give you any more on this, my solution isn't the ideal way, it's just a way of getting an answer. (I seem to have the equations of motion stuck in my head )

 

[hogrampage]

@kuruman, t is how long it takes to fall 100m. I just used a different method from jarednjames, but both are the same (4.52 s)

@jarednjames, It gave no dimensions. The question is exactly as I stated. That's what is confusing me.

 

[kuruman]

Is the horizontal velocity of the bomb changing?
Is the horizontal velocity of either plane changing?

 

[JaredJames]

The bomb will fall in an arc (ignoring air resistance), and so to simplify it you could look at it like a straight line descent with linear horizontal deceleration.

kuruman, this is what's confusing me, without being given the planes speed, you could assume it is traveling at what ever you like. Now I'm not sure, but no matter what the initial speed of the aircraft and you ignore air resistance, the deceleration will always be the same, and so no matter what speed you choose you will always get an answer that shows whether or not it will hit the lower aircraft.

 

[JaredJames]

For horizontal:

You know initial speed of bomb (u) = aircraft speed, time = (t) from part a. If you are ignoring air resistance (we did in part a so you should here), the bomb is not going to slow down, so (v) = (u). You now know v, u and t.

Using s = 0.5(u + v)t = (aircraft speed) x (time it takes the bomb to drop 100m)

Where s = horizontal distance travelled, you can calculate the distance the bomb will have moved horizontally at the 100m mark.

Using this with the first section, you can see whether or not they will intercept.

 

[kuruman]

If you ignore air resistance, the horizontal acceleration of the bomb is zero, i.e. it matches the horizontal velocity of the plane that launched it. There is no deceleration in the horizontal direction. Since the horizontal velocity of the plane below is also the same, this means that ... ?

 

[JaredJames]

Exactly, you end up with a collision, because the bomb travels the same distance as the plane would in the same time.

The key here is wind resistance, because that is all that acts to slow the bomb down. However, we ignored it in the first section so we should here.

It doesn't matter what speed the bombers travel at, without wind resistance, there will always be a collision.

I think the answer is that it would because of this. Under realistic circumstances, it wouldn't because the bomb would have slowed down due to air resistance and would miss the lower bomber.

 

[hogrampage]

So, ignoring wind resistance the bomb would hit the other plane, but with wind resistance it would not hit the other plane? I think I understand it now.

Thanks for the help :). It was really confusing me.