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# A ball of mass 'm' moves normal to a wall with a velocity 'u' and rebounds with a velocity 'v'. The change in momentum of the ball is (surface of the wall is smooth):m(u+v) towards the wallm(u+v) away from the wallm(u−v) towards the wallm(u−v) away from the wall

A
m(uv) towards the wall
B
m(u+v) away from the wall
C
m(u+v) towards the wall
D
m(uv) away from the wall
Solution
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#### A ball of mass, m, moving with initial velocity, u to the right towards a wall. It will have momentum →pi=m→u towards the right.The ball bounces off the wall. It will now be moving to the left, with the same mass, but a different velocity, v and therefore, a different momentum,→pf=m→v towards the left.The final momentum vector must be the sum of the initial momentum vector and the change in momentum vector, △→p=m−→△v . Using tail to head vector addition, △→p, must be the vector that starts at the head of →pi and ends on the head of →pf, hence the resultant change in momentum vector will point towards the left, that is, away from the wall.We also know from algebraic addition of vectors that:→pf=→pi+△→p→pf−→pi=△→pMagnitude of the change in momentum = mv−(−u)=m(v+u)Direction of change in momentum is towards the left, away from the wall.

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