Physics - Collisions in 2D

What is the formula for the vertical component of a momentum $p$?

\[p\sin\theta\]

What is the formula for the horizontal component of a momentum $p$?

\[p\cos\theta\]

If an object with mass $m _ 1$ is travelling in a straight line with velocity $v _ 1$, what is its momentum?

\[m_1v_1\]

If an object with mass $m _ 1$ is travelling at an angle $\theta _ 1$ to the $x$ direction with velocity $v _ 2$, what is its momentum?

\[m_1v_1\cos\theta_1\]

What is true about $\theta _ 1$ and $\theta _ 2$ for two identical masses in a 2D collision?

\[\theta_1 + \theta_2 = 90^{\circ}\]

If two objects have the same mass, what angle do they make with each other in a 2D collision?

\[90^{\circ}\]

What is true about momentum in a 2D collision?

It is conserved in both the $x$ and $y$ directions.

How are collisions in 2D similar to projectiles?

You treat the horizontal and vertical components seperately.

What is the vertical component of momentum for an object moving only in the $x$ direction?

\[0\]

After a collision, one object has mass $m _ 1$ and velocity $v _ 2$ at an angle of $\theta _ 1$. The other object has a mass $m _ 2$ and velocity $v _ 3$. What is the horizontal component of momentum after the collision?

\[m_1v_2\cos\theta_1 + m_2v_3\cos\theta_2\]

After a collision, one object has mass $m _ 1$ and velocity $v _ 2$ at an angle of $\theta _ 1$. The other object has a mass $m _ 2$ and velocity $v _ 3$. What is the vertical component of momentum after the collision?

\[m_1v_2\sin\theta_1 + m_2v_3\sin\theta_2\]

\[m _ 1v _ 2\sin\theta _ 1 + m _ 2v _ 3\sin\theta _ 2 = 0\]

How could you rewrite this?

\[m_1m_2\sin\theta_1 = -m_2v_3\sin\theta_2\]

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