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Hello All,

The following may be a simple problem. But, your thoughts will be very much appreciated.

Let's use a gun with mass m

Because the momentum is conserved, m

Hence, v

Now, I want to transform the same problem to the gun's frame of reference. (Hypothetically, it's an ant or a small person sitting at the muzzle observing the event!)

In this new frame of reference, the bullet moves at the following final speed: v

m

This means that v

Clearly, the answer from the first frame should be equal to the answer in the second frame.

Can someone please indicate to me where my working is incorrect?

Thanks in advance.

Quantised

The following may be a simple problem. But, your thoughts will be very much appreciated.

## Homework Statement

Let's use a gun with mass m

_{1}and a bullet m_{2}. The bullet is fired in the positive direction with speed v_{2}, and the gun recoils in the negative direction with speed v_{1}.Because the momentum is conserved, m

_{1}v_{1}= m_{2}v_{2}.Hence, v

_{2}can be calculated if m_{1}, m_{2}and v_{1}are all known. In other words, v_{2}= m_{1}v_{1}/ m_{2}. This calculation is from a stationary observer's frame of reference, outside the gun/bullet system.## Homework Equations

Now, I want to transform the same problem to the gun's frame of reference. (Hypothetically, it's an ant or a small person sitting at the muzzle observing the event!)

In this new frame of reference, the bullet moves at the following final speed: v

_{b, final}= v_{2}- v_{1}. The initial speed v_{initial}is zero, because the gun and the bullet are stationary. Therefore:m

_{2}(v_{2}- v_{1}) = (m_{1}+ m_{2}) v_{initial}= 0This means that v

_{1}= v_{2}.## The Attempt at a Solution

Clearly, the answer from the first frame should be equal to the answer in the second frame.

Can someone please indicate to me where my working is incorrect?

Thanks in advance.

Quantised

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