# Finding the CORRECT way to solve for Impulse in 2D Collisions [closed]

Firstly, my apologies as I forgot this website does not allow Check My Work type of discussions. Thank you to those who answered the reasonings by the way,

Basically, my question was as follows:

In a 2D collision, is there a reason why you cannot find the resultant velocities of an object before and after a collision and use that to find impulse? Why do you have to find each impulse component first using a change in velocity for x and y) before you solve using Pythagorean theorem?

• You've actually done what you're saying Commented Oct 12, 2023 at 13:24

Recall that impulse is defined as $$\vec{J} = \vec{P}_f - \vec{P}_i$$ If you just want the magnitude, you can consider the magnitude of both sides of the equation above $$|\vec{J}| = |\vec{P}_f - \vec{P}_i|$$ For any two vectors in general $$| \vec{P}_f - \vec{P}_i| \neq | \vec{P}_f| - | \vec{P}_i |$$ A good example to consider is two opposite pointing vectors, say $$\vec{A} = 4 \hat{i}$$ and $$\vec{B} = -4\hat{i}$$. Here, $$\vec{A} - \vec{B} = 8\hat{i}$$. So, $$| \vec{A} - \vec{B}| =8$$ while $$| \vec{A}| - | \vec{B}|=0$$. Since you want the magnitude of the impulse, you must find the vector $$\vec{P}_f - \vec{P}_i$$ first and then find its magnitude with Pythagoras and not the other way around.