# Submarine Fires Torpedo, Submarine's Recoil?

## Homework Statement

A submarine of mass 2.5 x 10^6 kg and initially at rest fires a torpedo of mass 260 kg. The torpedo has an initial speed of 100.4 m/s. What is the initial recoil speed of the submarine? Neglect the drag force of the water.

m1v1=-m2v2

## The Attempt at a Solution

mass one = 2.5x10^6 (submarine)
velocity one = 0 (sub isnt moving)
mass two = 260 (torpedo)
velocity two = 100.4 (torpedo)

How can I find the recoil? I thought maybe it'd just be velocity one (instead of zero solve for x)

v1 = (260*100.4)/2.5x10^6 = -0.01 m/s
But that's wrong...

what am i missing?

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I think you have the right idea, but you need to do it like this:

m1v1 (of sub) + m1v1 (of torpedo) = m2v2 (of sub) + m2v2 (of torpedo)
and since initial velocity of the sub is 0

m1v1 (of torpedo) = m2v2 (of sub) + m2v2 (of torpedo)

I think this is right, hope this helps!

LowlyPion
Homework Helper

## Homework Statement

A submarine of mass 2.5 x 10^6 kg and initially at rest fires a torpedo of mass 260 kg. The torpedo has an initial speed of 100.4 m/s. What is the initial recoil speed of the submarine? Neglect the drag force of the water.

m1v1=-m2v2

## The Attempt at a Solution

mass one = 2.5x10^6 (submarine)
velocity one = 0 (sub isnt moving)
mass two = 260 (torpedo)
velocity two = 100.4 (torpedo)

How can I find the recoil? I thought maybe it'd just be velocity one (instead of zero solve for x)

v1 = (260*100.4)/2.5x10^6 = -0.01 m/s
But that's wrong...

what am i missing?
They are asking for speed and not velocity. So I would expect they are not looking for a negative number.

Yeah, but if we have:

m1v1 (of torpedo) = m2v2 (of sub) + m2v2 (of torpedo)

doesnt m1v1 (torpedo) = m2v2 (torpedo) ? thus you'd just subtract one from the other, giving zero, resulting in:

0 = m2v2 (of sub)

Result would be undefined. What am I missing?

Initially in the problem, before the torpedo is fired, what is the momentum of the system? The total momentum after the torpedo is fired must be the same.

so for m1v1 (torpedo) is the initial mass the sub plus the torpedo?

Not sure I follow, can you be more specific?

Yes it would be. However, I think you're missing the point. The sub initially has no velocity, and the torpedo initially has no velocity. Therefore, what is the initial momentum of the system?

zero...

That's correct. If the initial momentum of the system is zero, then because of the conservation of momentum, the final momentum of the system must be zero. Does that help you at all?

I still don't get it...

Initial Momentum of System (aka zero) = m_sub*v_sub + m_torpedo*v_torpedo

Rearrange:

- m_sub*v_sub = m_torpedo*v_torpedo

Resulting in:

- (2500000)(recoil) = (260)(100.4)

-Recoil = ((260)(100.4))/2500000 = -0.0104416, which isn't accepted answer...

Do you happen to know what the correct answer is? How do you know it's not the accepted answer?

Our assignments are administered online via webassign.com.

It says -0.01 is wrong...

Have you tried it without the negative sign? And/or with more or less significant figures? I don't know why that answer would be wrong. However, if you're required to have the correct number of significant figures based on the problem, your answer should be 0.010.

I hope one of these solutions works for you

Odd...

The program allows for a 2% error and I've tried with any number of significant figures/variations (this is just practice, so I can try as many times as I want with no penalty)

Just frustrating because I understand all other recoil problems except this one...

LowlyPion
Homework Helper
Our assignments are administered online via webassign.com.

It says -0.01 is wrong...
And do they say + .01 is incorrect?

Yes,

These are wrong:
-0.01
0.01
0.010, etc
0.01044etcetc

Very odd