Cofused with this Momentum problem

[teken894]

19. Incorrect In a combustion engine, gas is burned. The resulting explosion produces a force that drives the pistons in the engine. The force of the explosion on the piston is due to the change in momentum of the gas molecules. A 0.4-g sample of gas produces a force of 2400 N in an explosion that lasts 10e-3 seconds. What must be the speed of the gas molecules?

My answer: 6 x 10e3 m/s
The correct answer: 3 x 10e3 m/s

I used the impluse force = change in momentum formula

ft = mv

2400(10e-3) = .0004(x)
and solved to get 6e3 m/s

What am I missing?

 

[lightgrav]

the molecules don't stick to the piston, they bounce off.
so the change of momentum is ( p_f - p_i ) double the final momentum.

 

[teken894]

Err...

I get that...but how is the answer 3e3 m/s ?

could you put some numbers into the explanation, because conceptually I'm not getting why the change the velocity is 3e3??

 

[lightgrav]

suppose the molecule is above the piston, calling upward as positive.
v_i is negative "v" , but v_f is positive "v".
The change of momentum is m times 2"v".

The change of momentum of the molecules is the negative of
the change of momentum of the piston (I expect you DID get this).