Consider a ball of mass 'm' moving with velocity 'v' and striking a wall, and it rebounds after striking. Assume, the collision is elastic. Now, if i have to find the force on the ball, that would be equal to rate of change of momentum of the ball. This is where, i have trouble, since momentum is a vector quantity therefore the change in momentum should be the vector sum of initial and final momentum. The initial momentum would be $mv$ along positive x-axis, and after collision it will be $mv$ along the negative x-axis. Since the two vectors are at 180° angle, therefore momentum change should be zero.
But if i calculate the momentum change as,
Final momentum - Initial momentum $= m (V_2-V_1) = m[-v - (v)] = -2mv$.
The second answer is right, but what is the flaw in the first approach?