Conservation of Momentum Problem

[jli10]

Homework Statement

A ball of mass $m_1$ travels along the x-axis in the positive direction with an initial speed of $v_0$. It collides with a ball of mass $m_2$ that is originally at rest. After the collision, the ball of mass $m_1$ has velocity ${v_1}_{x}{\hat{x}}+{v_1}_{y}{\hat{y}}$ and the ball of mass $m_2$ has velocity ${v_2}_{x}{\hat{x}}+{v_2}_{y}{\hat{y}}$. Consider the following five statements:

I) $0=m_1{v_1}_x+m_1{v_2}_x$
II) $m_1v_0=m_1{v_1}_y+m_2{v_2}_y$
III)$0=m_1{v_1}_y+m_2{v_2}_y$
IV) $m_1v_0=m_1{v_1}_x+m_1{v_1}_y$
V) $m_1v_0=m_1{v_1}_x+m_2{v_2}_x$

Of these statements, the system must satisfy
a) I and II
b) III and V
c) II and V
d) III and IV
e) I and III

Homework Equations

$(mv)_i=(mv)_f$

The Attempt at a Solution

I've never learned how to incorporate conservation of momentum into a 3-d plane...

 

[PeterO]

Homework Statement

A ball of mass $m_1$ travels along the x-axis in the positive direction with an initial speed of $v_0$. It collides with a ball of mass $m_2$ that is originally at rest. After the collision, the ball of mass $m_1$ has velocity ${v_1}_{x}{\hat{x}}+{v_1}_{y}{\hat{y}}$ and the ball of mass $m_2$ has velocity ${v_2}_{x}{\hat{x}}+{v_2}_{y}{\hat{y}}$. Consider the following five statements:

I) $0=m_1{v_1}_x+m_1{v_2}_x$
II) $m_1v_0=m_1{v_1}_y+m_2{v_2}_y$
III)$0=m_1{v_1}_y+m_2{v_2}_y$
IV) $m_1v_0=m_1{v_1}_x+m_1{v_1}_y$
V) $m_1v_0=m_1{v_1}_x+m_2{v_2}_x$

Of these statements, the system must satisfy
a) I and II
b) III and V
c) II and V
d) III and IV
e) I and III

Homework Equations

$(mv)_i=(mv)_f$

The Attempt at a Solution

I've never learned how to incorporate conservation of momentum into a 3-d plane...

This looks like only 2-D to me?

 

[jedishrfu]

write down the initial total momentum

then write down the final total momentum

then group the X components into one eqn and the Y components in another and see whether you can answer the question.

show your work and we can help

 

[jli10]

Whoops, sorry, I meant 2-d.
But I think I understand now... You just have to do conservation of momentum for each axis, right? Since the initial momentum is all in the x-direction, the final momentum for the y-components must sum to 0, which is shown in equation III. The initial x-momentum is given by $m_1v_0$, so the sum of components for the final x-momentum should be exactly that, given by equation V. Final answer (B).

 

[PeterO]

Whoops, sorry, I meant 2-d.
But I think I understand now... You just have to do conservation of momentum for each axis, right? Since the initial momentum is all in the x-direction, the final momentum for the y-components must sum to 0, which is shown in equation III. The initial x-momentum is given by $m_1v_0$, so the sum of components for the final x-momentum should be exactly that, given by equation V. Final answer (B).

That is correct.