Question

You hang from a tree branch, then let go and fall toward the Earth. As you fall, the y component of your momentum, which was originally zero, becomes large and negative. (a) Choose yourself as the system. There must be an object in the surroundings whose y momentum must become equally large, and positive. What object is this? (b) Choose yourself and the Earth as the system. The y component of your momentum is changing. Does the total momentum of the system change? Why or why not?

Short answer

a) Object in the case is the earth.

b) The total momentum of the system does not change.

Step-by-step solution

Significance of conservation of momentum 

Any contact between two objects that occurs in an isolated system conserves momentum

Selecting the object

(a)

It is traveling to an object that is imparting force to us, which is the earth.

Total momentum of the system

(b)

The change of momentum of system 1 is equal to equal and opposite to the change of momentum of system 2.

$∆P_{US}=-∆P_E$

Where$∆P_{U5}$ is the change of momentum of system 1.

$∆P_E$ is the change of momentum of the system 2.

Whereas the total momentum of the system is equal to the sum of the change momentum of system 1 and system 2.

So as per the law of conservation of momentum, the total momentum of the system is,

$∆P_{U5}+∆P_E=0$

Thus, the total momentum of the system does not change.