What formula do I use when dealing with collision, and momentum in this context?

[zedx]

Homework Statement

An object of mass m moving in a certain direction has a kinetic energy of 4.0 J.
It hits a wall and comes back with half its original kinetic energy.

Homework Equations

If the speed of the object on return is 2.0 m/s, what is the mass of the object?
A) 2.8 kg
B) 3.8 kg
C) 1.0 kg
D) 4.0 kg

The Attempt at a Solution

let mass of object = m
speed on return =2
kinetic energ on return = 0.5 m *v*v
kinetic energy initial =0.5*m*v1*v1
kf=0.5 ki
therefor v1= (2)^0.5 v
v1 =2.828 m/s

initial kinetic energy = 4 j
4=0.5*m*v1^2
8=m* 8
m=1 kg

My problem:
I don't understand the solution, nor what formula to use. Please help. Thanks.
I need to know why Answer: C is correct.

 

[ap123]

You're told that the final KE is 2.0J
You're told the speed, so use the formula for KE to solve for the mass.

This has nothing to do with momentum, only KE

 

[zedx]

So I should use KE = 1/2 m * v^2 to solve this problem, correct?

And I should solve for the mass, correct?

 

[zedx]

KE=1/2m*v^2,
KE =kinetic energy,
m=mass,
v=velocity

Mass comes back with half of its kinetic energy.
Its initial KE=4 so on the way back it's equal to 2

KE=2=1/2m*v^2 multiply each side by 2:
4=m*v^2, v=2m/s so v^2=4:
4=m*4 divide each side by 4
m=1.0 kg



Got the answer. Thanks.