An NFL place kicker is practicing his extra-point kicks. He kicks
the football into the wall of his living room and it hits at a speed
of 83 mph (or 37.1 m/s). If the wall did not move at all, how fast
would the ball bounce back? (Assume a perfectly elastic
collision and ignore friction.)

83 mph

Explanation:

We are told that the collision is perfect elastic, this means that no energy whatsoever was lost in the process.

We can apply the principle of conservation of momentum. It states that the total final momentum is equal to the total initial momentum in a system.

Hence, if the mass of the wall is assumed to be M and the mass of the ball is assumed to be m, we have that:

(M * V) + (m * v) = (M * U) + (m * u)

Where V = final velocity of Wall = 0 mph

v = final velocity of ball

U = initial velocity of wall = 0 mph

u = initial velocity of ball = 83 mph

Hence:

(M * 0) + (m * v) = (M * 0) + (m * 83)

=> mv = m * 83

=> v = 83 mph

The ball would have a final velocity of 83 mph.

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