Thank you so much for the nice compliment.

no, equation (3') is about v1f v2f and v1i satisfied an equations, they has nothing to do with the angle to be 90. v1f v2f and v1i are numbers not vectors so they have no direction. Imagine this: after colliding ball 2 somehow goes a wrong directions but v2f still the same, then equation (3') still satisfied. Or second way to understand: You need both momentum and energy equations for this answer, meanwhile equation (3') only for energy. The algebraic manipulation is just getting information from momentum equations and it strictly necessary

If the masses are different the angle will NOT be 90 degrees.

If masses are the same the angle must be 90.

😂 I tried to answer your question and then realized it was one year ago! I hope you already got the answer. What I’m thinking is that this video is for perfect elastic collision. But your case is not a perfect elastic one, which involves restitution coefficient, 0

Use sine law

Thank you

Thank you! 🙂

Yes!

Unless it’s a head on collision of course.

@@PhysicsNinja what about different mass?

@@amirrafiqi7232 Mathematically more difficult but write down conservation of momentum and kinetic energy and solve for the 2 final velocities. In this case the angle will depend on the masses.

@@amirrafiqi7232 In 2D collisions, you can only have elastic collisions between objects of the same mass.

I took the sign into consideration when I wrote the conservative of momentum.

Your problem doesn’t say that the collision is elastic. If it’s not elastic than it’s a different problem

I have several courses on Udemy. Use code PHYSICS999 to get the lowest price.

Thank you. Physics Ninja loves new subscribers.

deez nuts

This guy is one curious cat! Can he be helped please?

@@pgille2 the idea is if a = x and b = y then a + b = x + y ( the same concept of adding like this also works with subtraction, division and multiplication)

Momentum is a vector quantity.. depending on the direction you take as +ve (in the video, + y is the positive direction), the vector quantity in the opposite direction will be - ve

@@5alidtheog924 Since the angle is formed below the x-axis, and suppose the angle is -30*(which is formed by going clockwise), you can also write that as 330* in standard position(which just means that that you form the triangle by going counter-clockwise). You would still get the same answer because sin(-30*) and sin(330*) are the same which would be negative 1/2. When he put - [sin(-30*)] it becomes -(-1/2) which then becomes 1/2. That is wrong because it now becomes moving in the positive direction when it is actually moving in the negative direction.He put the negative first because it actually is but when you put in the angle, you get 2 negatives when you just want 1 negative. It should be +m1*vf*sin(-30*)

Almost. You won't get the right answer if the angle theta =0 ( a head on collision). The general solution works for all cases.

Kinetic energy is a scalar NOT a vector, it has no direction, it’s just a number.

@@PhysicsNinja thank you a lot

You probably already know now but the angles do not add up to 90 degrees

I would like to see an example that uses the example of dart satellite impacting with didymos b. A fascinating real world example

This works nicely for the case of the same mass. It doesn’t work for the case of different masses.

Same approach just more math. The masses will not cancel out if they are different.

No, this formula assumes the mass of the balls are equal.

@@PhysicsNinja yes thats what I needed to know thank you

*Wasted 😐

m1, m2 masses, v1, v2 initial velocities, u1, u2, final velocities, then you have conservation of momentum for both axes, for the momentum is a vector. For the X axis you have m1 * v1x + m2 * v2x = m1 * u1x + m2 * u2x. You can do the same for the Y component. Now, you also have conservation of kinetic energy, if we talk about elastic collision ( there's no deformation, so no loss of kinetic energy ), so you have 1/2 * m1 * v1^2 + 1/2 * m2 * v2^2 = 1/2 * m1 * u1^2 + 1/2 * m2 * u2^2. Using these three equations you can find all the information you need. Don't forget about that vector components can be written using sin and cos. I am actually trying to simulate collision in 2D using JavaScript so I have to relearn all of this, still learning.