1. ## Momentum Problem

Bullet of mass 0.05 kg is fired from a gun with velocity 700 m/s, find the momentum of the gun immediately after it's fired?

I used Momentum = mv = $-35 kg m/s$? - Here I'm taking the direction of the bullet as positive.

If the gun is brought to rest in 1s by a horizontal force that rises uniformly from 0 to Z N, then falls uniformly back to 0 again, find the value of Z.

No idea how to start this really. Was thinking to try and find the average acceleration and then use $F = ma$, however the acceleration isn't constant, so this wouldn't work would it?

Would love it if someone could give me a little pointer on this?

2. Let $f(t)$ represent the force on the gun. Then the impulse is equal to the change in momentum:

$\int _0 ^1 f(t) \cdot dt = 35 \frac{kg \cdot m}{s}$

Since the force increases and decreases uniformly,

$\int _0 ^{0.5} f(t) \cdot dt = \int _{0.5} ^1 f(t) \cdot dt = 17.5 \frac{kg \cdot m}{s}$

And f(t) is the equation of a line from 0 to 0.5: f(t) = kt + c

But c = 0 since f(0) = 0,

so solve $\int _0 ^{0.5} kt \cdot dt = 17.5$ for k.

Then $Z = 0.5k$.

3. Again sorry for the late reply.

Thanks a lot for your reply, would have never thought to do it this way.

Solving the integral above you get $\frac{k}{8} = 17.5$, $k = 140$.

Putting this back into the equation of the line, we get the value of Z to be 70?

Thanks again for the help

4. Yes, the value of Z is 70.

5. Thanks again, your a life saver!