Calculating the average force of a molecule in a vessel

[PhyIsOhSoHard]

Homework Statement

Suppose an oxygen molecule traveling at the speed of 484 m/s bounces back and forth between opposite sides of a cubical vessel 0.1 m on a side. What is the average force the molecule exerts on one of the walls of the container?

Homework Equations

F=p/t

The Attempt at a Solution

t=0.2 m / 484 m/s = 4.13 *10^-4 seconds

In a collision v changes direction so delta p = 2*mv

(mv was calculated in a previous question so it is known)

The average force can then be calculated as:

F = 2mv / t

My question here is, how come when calculation the time, they use 0.2 m and not 0.1 as given in the assignment? Is this because the molecule moves back and forth 0.1 m during the collision?

Second question: why do they multiply a factor 2 on the impulse? Where does this come from?

 

[haruspex]

They are considering impacts on a given wall. How far does the molecule travel between successive impacts there?
Each impact, the molecule strikes the wall with velocity v, head on, and bounces back. What is the net change in velocity?