Final answer:
The velocity of the tackler after an elastic collision with the halfback is calculated using the conservation of momentum. After performing the calculations, the tackler is found to be moving at 2.72 m/s to the left.
Step-by-step explanation:
Calculating the Velocity of the Tackler After Elastic Collision
To solve the problem of finding the velocity of the tackler after an elastic collision with the halfback, we can use the conservation of momentum which states that the total momentum before the collision is equal to the total momentum after the collision. Since this is an elastic collision, kinetic energy is also conserved.
The initial momentum can be calculated using the formula: p = mv, where m is mass and v is velocity. The initial momentum of the tackler (110 kg) moving at 2.5 m/s to the right is ptackler_initial = 110 kg * 2.5 m/s = 275 kg*m/s. The halfback (82 kg) moving at 5.0 m/s to the left (which we'll take as negative for direction) has an initial momentum of phalfback_initial = 82 kg * -5.0 m/s = -410 kg*m/s.
The total initial momentum is ptotal_initial = ptackler_initial + phalfback_initial = -135 kg*m/s.
After the collision, the halfback moves to the right at 2 m/s, thus his momentum becomes phalfback_final = 82 kg * 2 m/s = 164 kg*m/s. To find the velocity of the tackler after the collision, we set the total final momentum equal to the total initial momentum and solve for the tackler's final momentum:
ptackler_final = ptotal_initial - phalfback_final
ptackler_final = -135 kg*m/s - 164 kg*m/s = -299 kg*m/s
The negative sign indicates the tackler is now moving to the left. Finally, we find the velocity of the tackler by dividing his final momentum by his mass:
vtackler_final = ptackler_final / mtackler = -299 kg*m/s / 110 kg = -2.72 m/s
Therefore, the tackler's velocity after the collision is 2.72 m/s to the left.