# Momentum in 2 Dimensions

1. Apr 12, 2010

### Procrastinate

A radioactive nucleus of mass 5 × 10–26 kg is at rest and emits two neutrons,
each of mass 1.6 × 10–27 kg, at right angles to each other. If both have speeds of
360 m s–1, calculate the recoil speed of the nucleus.

I named calculated the neutrons and named them p1 and p2.
Since p1 = p2
Therefore the momentum of both equals 1.8x10-26

Using Pythagoras, I worked out the overall momentum to be 2.55x10-26

I then used the formula m1v1 = m2v2 and worked out the velocity to be 509-510ms-1; I didn't bother working out the angle because that was already the wrong answer. The real answer is 17.39ms-1.

What have I done wrong? Thanks in advance.

2. Apr 12, 2010

### rl.bhat

Therefore the momentum of both equals 1.8x10-26

Using Pythagoras, I worked out the overall momentum to be 2.55x10-26

Check these two calculations. They are wrong.

3. Apr 12, 2010

### Procrastinate

It turns out I just got mixed up with the numbers and exponents. Thanks.

Is my formula for this correct by the way (I'll count the two neutrons as one mass)?

m1u1 + m2u2 = m2v2 + m2v2

4. Apr 12, 2010

### rl.bhat

The formula is correct. The left hand side is zero. After emission the mass of the nucleus is reduced by two times the mass of the neutrons.