In Times Square in New York City, people celebrate on New Year's Eve. Some just stand around, but many move about randomly. Consider a system comprised of all of these people. Approximately, what is the total linear momentum of this system at any given instant?

The total linear momentum at any time is zero.

Explanation:

Hi there!

The momentum of an object is a vector that is calculated by multiplying the mass of the object times its velocity.

The momentum of the system is calculated by adding the momenta of each object that comprise the system (in this case, all the people in Times Square).

Since the people move randomly in all directions, it is most probable that the total momentum of the system is zero because the momentum vectors of people moving in one direction will surely be canceled by the momentum vectors of people moving in the opposite direction. In total, the sum of momentum vectors will be zero (the standing people have null momentum because their velocities are zero).