# Physics - Collisions in 2D

> Source: https://ollybritton.com/notes/a-level/physics/topics/collisions-in-2d/ · Updated: 2021-01-12 · Tags: physics, momentum, school, year-1

##### 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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