How Far Does a Bullet Travel When a Gun Recoils 2mm?

[kateman]

Homework Statement

A 500g pistol lies at rest on an essentially frictionless table. It accidentally discharges and shoots a 10g bullet parallel to the table. How far has the bullet moved by the time the gun has recoiled 2.00mm?

Homework Equations

0=m1v1+m2v2
m1v1= (m1+m2)Vf

The Attempt at a Solution

well i tried the 0=m1v1+m2v2 formula and tried to substitute the value of v as s/t and then eliminating time, i rearranged it for the displacement value of the bullet and got a weird value of -.1 when the answer is 9.8cm
i know now that this is the wrong way to approach it when i consider the conservation of momentum but i have no other ideas on how to do this or how to start it!

if anyone does it would be most appreciated!

 

[Doc Al]

There's nothing at all wrong with your approach, or even your answer, depending upon the units you are using. Realize that if the gun goes moves one way (+ say), then the bullet will move in the opposite direction (call it -).

0.1 m = 10 cm. If you subtract the 2 mm (0.2 cm) that the gun moved you'll get 9.8 cm. (But I see no reason why you would subtract the gun's movement from the bullet's, so I disagree with that answer.)

 

[Astronuc]

Well, the force pushing the bullet is pushing back on the gun.

So F=ma

then both bullet and gun are starting at rest, and force applied over distance (F*d) is energy, and the energy is kinetic.

Assume constant acceleration. The lighter mass accelerates faster.

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html

 

[kateman]

ahh yeah converting back to cm might help :P

hmm that's very interesting (what you found), but i agree, it does seem to be just a random coincidence

yup, its all good now, thanks to both of you

 

[Doc Al]

Also realize that the (perfectly valid) approach that you took is equivalent to noting that the center of mass of "bullet + gun" does not change. If the gun moves 2mm to the left, then the bullet must move 10 cm to the right to maintain the center of mass.

 

[kateman]

yeah i do now thanks