Answer :
Final answer:
Using the law of conservation of momentum, the mutual speed of the tackler and the halfback after the collision can be found to be approximately 4.23 m/s.
Explanation:
Using the law of conservation of momentum, we can find the mutual speed of the tackler and the halfback after the collision. The law of conservation of momentum states that the total momentum of a system before a collision is equal to the total momentum after the collision, assuming no external forces are acting on the system. In this case, the initial momentum of the tackler is given by:
Initial momentum of tackler = mass of tackler * velocity of tackler
= 110 kg * 2.4 m/s = 264 kg·m/s
The initial momentum of the halfback is:
Initial momentum of halfback = mass of halfback * velocity of halfback
= 93 kg * 6.4 m/s = 595.2 kg·m/s
Since momentum is conserved, the total initial momentum is equal to the total final momentum:
Total initial momentum = Total final momentum
264 kg·m/s + 595.2 kg·m/s = (mass of tackler + mass of halfback) * final velocity
859.2 kg·m/s = (110 kg + 93 kg) * final velocity
859.2 kg·m/s = 203 kg * final velocity
final velocity = 859.2 kg·m/s / 203 kg
final velocity ≈ 4.23 m/s
Therefore, the mutual speed of the tackler and the halfback immediately after the collision is approximately 4.23 m/s.
