Derive formula using Conservation of Energy and Momentum

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1. Mar 19, 2017

Unicorns812877

1. The problem statement, all variables and given/known data
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'

2. Relevant equations
Conservation of Energy
Conversation of Momentum

3. 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'

Last edited: Mar 19, 2017
2. Mar 19, 2017

haruspex

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

3. Mar 19, 2017

Unicorns812877

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

4. Mar 19, 2017

haruspex

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.

5. Mar 21, 2017

haruspex

Do you need more help?