# Math Help - Momentum and Velocity

1. ## Momentum and Velocity

hey, im new to the forum, im having a lot of trouble with my last engineering assignment,
If someone could point me in the right direction much applyed
Btw its a mechanical principles question.

Question: A nail gun of a mass of 2kg fires 20g nails; it experiences a retarding force of 50N and recoils by 1.25cm after each nail is fired. Find the initial speed of the nail leaving the gun.

So at the moment what i have worked out is...
Momentum before = momentum after
Mgn Vgn = Mg Vg + Mn Vn
Momentum before is 0 as nothing as nail hasnt been fired

To find V im using V2 = u2 + 2as (the first 2's are ment to be powers)
when s= displacement (i gaver this is recoil? so it would be 1.25cm)
u = inital velocity
v = final velocity
a = acceleration (A=F/M=50/0.02= 2500m/s)
t = time

Rep will be given, i need this assignment done for monday so i can stay on the college course im doing

2. You have figured out

$m_{gun}*u_{gun}=m_{nail}*u_{nail}$

only $u_{gun}$ is troubling you.

you have taken the correct steps

To find V im using V2 = u2 + 2as (the first 2's are ment to be powers)
when s= displacement (i gaver this is recoil? so it would be 1.25cm)
u = inital velocity
v = final velocity=0
a = acceleration (A=F/M=50/0.02= 2500m/s)
t = time
only this is that since this is retardation, $a=-\frac{F}{m_{gun}}=-25$

$v^2-u^2=2as$

giving
$u(=u_{gun})=\sqrt{2*25*.0125}$