Question

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?

Answer 1

In a two-dimensional collision, it is necessary to find the impulse components using the change in velocity for both the x and y directions before solving using the Pythagorean theorem. This allows us to determine the magnitudes and directions of the resultant velocities.

Step-by-step explanation:

In a two-dimensional collision, it is necessary to find the impulse components using the change in velocity for both the x and y directions before solving using the Pythagorean theorem. This is because in a two-dimensional collision, the velocities of the objects involved can change in both the horizontal and vertical directions.

By resolving the velocities into their components, we can determine the changes in momentum in each direction separately. This allows us to find the magnitudes and directions of the resultant velocities of the objects involved after the collision.

Using the Pythagorean theorem, we can then combine the components to find the magnitude of the resultant velocity and determine the direction using trigonometry.