Gun and Shell: Calculate Velocity and Force

[milan.007]

Homework Statement

A gun of mass 500Kg fires a shell of mass 2Kg with a muzzle velocity of 500m/s.
Calculate:
i) the velocity of recoil of the gun
ii) the force required to stop the gun in a distance of 0.25m

Homework Equations

The Attempt at a Solution

i)I got the velocity of the gun by using the principal of conservation of momentum:
(500)(0) + (2)(0) = 500v + (500)(2). I got 2m/s.

ii)First i used v=d/t, 2=0.25/t, I got 0.125 seconds.
Then i used Force = change in momentum/time taken.
I get 8000N but the book says 4000N.
Im not sure what I am doing wrong??

 

[tiny-tim]

First i used v=d/t …

Hi milan!

You've assumed the velocity is constant (at 2 m/sec).

That gave you the wrong value of t.

Can you see some other way to calculate t (from initial velocity, final velocity, and distance)?