
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
21) A particle of mass  $m$  moving at speed  $v_0$  collides with a particle of mass  $M$  which is originally at rest. The fractional momentum transfer  $f$  is the absolute value of the final momentum of  $M$  divided by the initial momentum of  $m$ .

If the collision is perfectly  $elastic$ , what is the maximum possible fractional momentum transfer,  $f_{max}$ ?

A)  $0 < f_{max} < \frac{1}{2}$ B)  $f_{max} = \frac{1}{2}$ C)  $\frac{1}{2} < f_{max} < \frac{3}{2}$ D)  $f_{max} = 2$ E)  $f_{max} \ge 3$ 

Present the answer in LaTex format: \boxed{Your answer}
user