Solving Elastic Collisions: 25g & 10g Objects

[kimlu]

Homework Statement

A 25g object moving to the right at 20cm/s overtakes and collides elastically with a 10g object moving in the same direction at 15 cm/s. Find the velocity of each object after the collision

Homework Equations

Ʃp=Ʃp'
v1+v1'=v2+v2'

The Attempt at a Solution

First I tried to find one one of the v primes by using the momentum equation

25(20)+10(15)=25v1'+10v2' and then simplifying it to
500+150=250(v1'+v2')
650-250v1'=v2'

Afterwards I plugged this in for v2' in v1+v1'=v2+v2' and solved through to get 2.57 cm/s for v1' which I know is incorrect. I know I did something wrong in the step above but I don't know how to approach this.

 

[ehild]

Homework Statement

A 25g object moving to the right at 20cm/s overtakes and collides elastically with a 10g object moving in the same direction at 15 cm/s. Find the velocity of each object after the collision

Homework Equations

Ʃp=Ʃp'
v1+v1'=v2+v2'

The Attempt at a Solution

First I tried to find one one of the v primes by using the momentum equation

25(20)+10(15)=25v1'+10v2' and then simplifying it to
500+150=250(v1'+v2')
650-250v1'=v2'

Afterwards I plugged this in for v2' in v1+v1'=v2+v2' and solved through to get 2.57 cm/s for v1' which I know is incorrect. I know I did something wrong in the step above but I don't know how to approach this.

The red part is wrong.

ehild

 

[kimlu]

The red part is wrong.

ehild

I'm not quite sure how to simplify that part it would help if you would tell me how :c

 

[ehild]

I'm not quite sure how to simplify that part it would help if you would tell me how :c

25v1'+10v2' is not 250(v1'+v2'). Isolate v2' from the equation 25v1'+10v2'=650, and plug in for v2' in v1+v1'=v2+v2'.

ehild