To find the mutual speed after the tackle, we use the conservation of momentum principle. Before the tackle, the combined momentum of the halfback and cornerback equals their combined momentum after the tackle.
First, we calculate the total momentum before the tackle by adding the momentum of the halfback and the cornerback:
Total momentum before = Halfback's momentum + Cornerback's momentum
= (80.00 kg × 4.10 m/s) + (85.0 kg × 5.50 m/s)
= 328 kg m/s + 467.5 kg m/s
= 795.5 kg m/s
Then, we set the total momentum before the tackle equal to the total momentum after the tackle:
Total momentum before = Total momentum after
795.5 kg m/s = (80.00 kg + 85.0 kg) × Mutual speed after
Solving for the mutual speed after the tackle:
Mutual speed after = 795.5 kg m/s ÷ 165 kg
Mutual speed after ≈ 4.82 m/s
So, the mutual speed immediately after the touchdown-saving tackle is approximately 4.82 m/s.
