How to find resulting velocity in a perfectly elastic collision?

[haha0p1]

Homework Statement

A particle of mass m travelling with velocity u collides elastically and head-on with a stationary particle of mass M. Which expression gives the velocity of the particle of mass M after the collision.

Relevant Equations

Momentum=Mass×Velocity

Using principle of conservation of momentum:
m×u=m×v1 + M×v2
Where m=mass of moving particle in the beginning
u=Initial velocity of particle m
v1= final velocity of particle m
v2=velocity of object M
m×u-(mv1)=Mv2
(mu-mv1)÷M=v2
My answer is this (mu-mv1)÷M
However, it is nowhere close to the correct answer. Kindly tell where I am going wrong in the calculation.

 

[haruspex]

You should not have v1 in the answer since that is also unknown. You have not used that the collision is perfectly elastic.

 

[haha0p1]

You should not have v1 in the answer since that is also unknown. You have not used that the collision is perfectly elastic.

I have used V1 im the equation because the initial momentum is equal to final momentum and V1 is a part of the final momentum.

 

[haruspex]

I have used V1 im the equation because the initial momentum is equal to final momentum and V1 is a part of the final momentum.

There's nothing wrong with it as an equation, but it is not acceptable as an answer. Only m, M and u are allowed. To eliminate v1 you need another equation, the equation for energy conservation.

 

[haha0p1]

Using principle of conservation of momentum:
mu=(m×v-u)+M×v
mu-m(v-u)=M×v
-mv÷M=v

Note:
m=mass of the initially moving object
v=velocity of object woth mass M
x-u=Velocity of object m after the collision

I have used a different method but I am still getting a wrong answer.

 

[kuruman]

If the different method does not include kinetic energy conservation as @haruspex suggested, you will keep getting a wrong answer. The initial momentum conservation equation you had

m×u-(mv1)=Mv2

is correct so leave it alone. Be sure to use subscripts to avoid confusion.