Afootball player runs at 8m/s and plows into a 80kg referee standing on the field causing the referee to fly forward at 5m/s. if this were a perfectly elastic collision, what would the mass of football player be?

The topic here is momentum.

When a collision is said to be elastic, it means that the colliding objects now travel at their own new, indivual and distinct velocities, often in different directions.

So we write that as,

(mass of football player x velocity of football player) + (mass of referee x velocity of referee) = (mass of football player x velocity of football player) + (mass of referee x velocity of referee)

(M × 8) + (80 × 0) = (M× 0) + (80 × 5)

8M = 400

M = 50 kg