# Homework Help: Linear Momentum Algebraic interpretation

1. Oct 29, 2014

### brycenrg

1. The problem statement, all variables and given/known data
A light object and a heavy object have the same kinetic energy. Which has more momentum?

2. Relevant equations
I am trying to prove this through algebra.
I don't understand how to show this any help?

3. The attempt at a solution
1/2m1v1^2 = 1/2m2v2^2 when m1 > m2

v1 = v2 squareroot(m2/m1)

m1v2 squareroot(m2/m1) = m2v1 squareroot(m1/m2)

2. Oct 30, 2014

### ehild

I do not see what is the sense of your last line. What are the momenta?

3. Oct 30, 2014

### Orodruin

Staff Emeritus
I suggest you work in the other direction and do not use v as a variable. Instead, solve for v from p = mv and insert this into the expression for kinetic energy.

4. Oct 30, 2014

### quantumtimeleap

Here's a hint. You do have to use algebra here, but this is only a qualitative question where you have to find the relationship

$\frac{KE_1}{KE_2} = constant = \alpha(m_1, m_2) \frac{p_1^2}{p_2^2}$

where $\alpha$ is a function of the two masses. Once you find this relationship, you can answer the question easily.

Goodluck!!! ;)