# Deriving the head-on collision equation in terms of v2' and v1'

• louise82
In summary, the conversation discusses deriving the head-on collision equation in terms of v2' and v1', and how to solve for v1' and v2' using the given equations. The solution involves plugging one equation into the other to eliminate one of the variables. The conversation concludes with the person realizing their mistake and feeling grateful for the help.

#### louise82

[SOLVED] Deriving the head-on collision equation in terms of v2' and v1'

I think I'm having an algebra issue here, but how is the momentum equation (where v2=0):

m1(v1-v1')=m2v2'

combined with v1+v1'=v2'

to give:

v2' = v1 [ 2m1/(m1+m2)]

and

v1' = v1 [(m1-m2)/(m1+m2)]

I'm realizing this must be an elementary question since my book doesn't actually show how they derive those equations, but I'm not seeing it.

Help someone?

Plug v2'=v1+v1' into the first equation, and then solve for v1'.

So... you have two equations... and you are trying to eliminate one of the variables?

Ok, I can find v1', but I'm confused on which equation to plug in where to get v2'.

They gave you v2' in terms of v1 and v1', did they not?

louise82 said:
Ok, I can find v1', but I'm confused on which equation to plug in where to get v2'.
There aren't very many options... why not try them all?

Ok, feel dumb now. But since I'm exposed I may as well ask all my other dumb questions. Thanks for the help. :)

louise82 said:
Ok, feel dumb now. But since I'm exposed I may as well ask all my other dumb questions. Thanks for the help. :)

Hey louise, you got it, so you should feel smart.

## 1. What is the head-on collision equation?

The head-on collision equation is a mathematical formula that represents the conservation of momentum in a head-on collision between two objects. It states that the total momentum before the collision is equal to the total momentum after the collision.

## 2. How is the head-on collision equation derived?

The head-on collision equation is derived by applying the principles of conservation of momentum and Newton's second law of motion. By equating the total initial momentum with the total final momentum, we can rearrange the equation to solve for the velocities of the two objects involved in the collision.

## 3. What is the significance of expressing the equation in terms of v2' and v1'?

Expressing the equation in terms of v2' and v1' allows us to solve for the velocities of the objects after the collision, rather than the velocities before the collision. This is useful in real-world scenarios where we may not know the velocities of the objects before the collision, but can measure their velocities after the collision.

## 4. Can the head-on collision equation be applied to all types of collisions?

No, the head-on collision equation is specifically designed for head-on collisions where the two objects involved have the same mass. For other types of collisions, such as oblique or elastic collisions, different equations and principles must be used.

## 5. Is the head-on collision equation always accurate?

The head-on collision equation is a simplified model that assumes ideal conditions, such as perfectly elastic collisions and point masses. In real-world scenarios, there may be factors such as friction and non-ideal elasticity that can affect the accuracy of the equation. Therefore, it should be used as a guide rather than an exact representation of the collision.