The momentum change of the running back is - 664.2 kg m/s or 664 west.
Explanation:
Momentum is defined as the change in velocity of any object along with its mass. So mathematically, momentum can be derived using the product of mass with the change in velocity.
[tex]\text { Momentum change }=m \times \Delta v[/tex]
As here mass is given as 82 kg and the initial velocity was 5.6 m/s and final velocity is 2.5 m/s.
Initial Momentum = [tex]m \times \text { initial velocity }=82 \times 5.6=459.2 \mathrm{kg} \mathrm{m} / \mathrm{s}[/tex]
Final Momentum = [tex]m \times \text { final velocity }=82 \times(-2.5)=-205 \mathrm{kg} \mathrm{m} / \mathrm{s}[/tex]
Momentum change = Final Momentum - Initial Momentum
Momentum change = - 205 - 459.2 = - 664.2 kg m/s or 664 west
Thus, the changing momentum is -664.2 kg m/s. The negative sign indicates that the momentum is acting in the opposite direction on changing in the direction of velocity.
