# Linear momentum/kinetic energy

1. Mar 22, 2006

### mb85

A certain radioactive (parent) nucleus transforms to a different (daughter) nucleus by emitting an electron and a neutrino. The parent was at rest at the origin of an xy coordinate system. The electron moves away from the origin with linear momentum (-3.3 x 10-22 kg m/s) ; the neutrino moves away from the origin with linear momentum (-2.2 x 10-23 kg m/s) . What are (a) the magnitude and (b) angle (from the +x axis) of the linear momentum of the daughter nucleus? (c) If the daughter nucleus has a mass of 1.8 x 10-26 kg, what is its kinetic energy?

i know part a and b i did are correct:
part a. i got 3.3x10^-22 kg m/s
part b the angle is 3.81 degrees

but i cant figure out part c? what formula am i supposed to use.

2. Mar 22, 2006

### neutrino

Do you know how to write down the kinectic energy of a particle in terms of its momentum?

3. Mar 22, 2006

### mb85

p = mv?

the KE = (m -mi)V^2

?

4. Mar 22, 2006

### neutrino

K.E = 1/2 mv^2 . Multiply and divide RHS by m. K.E = (mv)^2/2m

5. Mar 22, 2006

### mb85

what is RHS?
K.E = (mv)^2/2m
i get 9.8x10-70....but that doesnt look right.

6. Mar 22, 2006

### Libertine

Right hand side.

You start with $$K.E. = \frac{1}{2}mv^2$$

Then multiply both sides by m, but to keep them the same you must divide by m, i.e.:
$$K.E. = \frac{1}{2}mv^2 . \frac{m}{m}$$
$$K.E. = \frac{m^2 v^2}{2m}$$
$$K.E. = \frac{(mv)^2}{2m}$$
Then use the fact that $$p = mv$$ to get:
$$K.E. = \frac{p^2}{2m}$$

Can you use that formula to get the answer?

7. Mar 22, 2006

### mb85

thanks. i got it now.