Final answer:
To calculate the total momentum of the system, the individual momenta of you and the ball are summed. Your momentum is negative due to your direction of travel, and the ball's is positive. The magnitude of the total momentum of the system is 276.82 kg·m/s.
Step-by-step explanation:
To calculate the total momentum of the system consisting of you and the ball, we have to consider the momentum of each and add them together. Momentum is a vector quantity, given by the product of an object's mass and its velocity, with direction being important. Here, since both you and the ball are moving toward each other, we will treat your momentum as negative and the ball's momentum as positive.
First, we calculate your momentum using the formula p = mv where p is the momentum, m is the mass, and v is the velocity. For you, the momentum is p = (60 kg) * (-4.8 m/s) = -288 kg·m/s (the negative sign indicates direction). As for the ball, if we take a standard adult football as an example, it might weigh about 0.43 kg (though the exact weight isn’t given in the question). The momentum of the ball would be p = (0.43 kg) * (26 m/s) = 11.18 kg·m/s.
Finally, to find the total momentum of the system, we add your momentum and the ball’s momentum: -288 kg·m/s + 11.18 kg·m/s = -276.82 kg·m/s. The magnitude of the total momentum is the absolute value of this number, which is 276.82 kg·m/s.