Derive formula using Conservation of Energy and Momentum

[Unicorns812877]

Homework Statement

Playing in the street, a child accidentally tosses a ball (mass m) with a speed of v=23 m/s toward the front of a car (mass M) that is moving directly toward him with a speed of V=20 m/s . Treat this collision as a 1-dimensional elastic collision. After the collision, the ball is moving with speed v′ back toward the child and the car is moving with speed V′ in its original direction.

My options are:
A) v + V = v' - V'
B) v - V = -v' + V'
C) v - V = v' -V'
D) v + V = -v' + V'

Homework Equations

Conservation of Energy
Conversation of Momentum

The Attempt at a Solution

I took the movement of the child's ball as the positive direction and the car's direction as the negative. So this would give me v - V = -v'-V' but that is not an option. Can someone point me in the proper direction?

EDIT:
For all of those coming for a quick answer for MasteringPhysics, the answer is v + V = v' -V'

 

[haruspex]

would give me v - V = -v'-V'

No, it wouldn't. These are not momentum equations. What law does the (correct) equation represent?

 

[Unicorns812877]

No, it wouldn't. These are not momentum equations. What law does the (correct) equation represent?

I want to say conservation of energy but I cannot for the life of me wrap my head around this question.

 

[haruspex]

I want to say conservation of energy but I cannot for the life of me wrap my head around this question.

The equation, in its more general form, is known as Newton's Experimental Law. The form here is for the special case where KE is conserved, i.e. the coefficient of restitution is 1. It can be derived from the laws of conservation of energy and momentum, but is simpler than either.
See https://en.m.wikipedia.org/wiki/Coefficient_of_restitution.

 

[haruspex]

Do you need more help?