(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The following mathematical model was suggested for the variation in pressure inside the 10-mm-diameter barrel of a rifle as a 25-g bullet was fired:

[tex]p(t)=(950MPa)e^{-t/(0.16ms)}[/tex]

where t is expressed in ms. Knowing that it took 1.44 ms for the bullet to travel the length of the barrel and that the velocity of the bullet upon exit was measured to be 520 m/s, determine the percent error introduced if the above equation is used to calculate the muzzle velocity of the rifle.

Answer:

8.18%

2. Relevant equations

[tex]mv_1+\int_{t_1}^{t_2}F(t)dt=mv_2[/tex]

Percent error = [|actual-experimental|/|actual|]*100

3. The attempt at a solution

We are given the experimental v_{2}and are asked to find the "actual" v_{2}using the mathematical model, then the percent error between them.

[tex]\left ( .025 \right )\left ( 0 \right )+\int_{0}^{.00144}950 \cdot 10^6e^{-t/.00016}dt=\left (.025 \right )\left (v_2 \right )[/tex]

[tex]v_2=\frac{\frac{-950 \cdot 10^6}{.00016}e^{-.00144/.00016}}{.025}[/tex]

This yields a number around -29 billion... Not even close to 520 m/s.

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# Bullet velocity using impulse-momentum

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