1
$\begingroup$

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?

$\endgroup$
1
  • $\begingroup$ You've actually done what you're saying $\endgroup$
    – khaxan
    Oct 12, 2023 at 13:24

1 Answer 1

1
$\begingroup$

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.

$\endgroup$
1
  • 1
    $\begingroup$ Thank you so much! I figured it was an order of operations type issue. $\endgroup$ Oct 13, 2023 at 16:24

Not the answer you're looking for? Browse other questions tagged or ask your own question.