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22 PE

Expert-verifiedFound in: Page 82

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of **\({\bf{6}}{\bf{.20 \times 1}}{{\bf{0}}^{\bf{5}}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\)** ****for**\({\bf{8}}{\bf{.10 \times 1}}{{\bf{0}}^{{\bf{ - 4}}}}\;{\bf{s}}\)** ****. What is its muzzle velocity (that is, its final velocity)?**

The muzzle velocity of bullet is \(502.2\;{\rm{m/s}}\).

Given Data:

The initial velocity of bullet is \(u = 0\)

The time for acceleration of bullet is \(t = 8.10 \times {10^{ - 4}}\;{\rm{s}}\)

The acceleration for bullet is \(a = 6.20 \times {10^5}\;{\rm{m}}/{{\rm{s}}^2}\)

**The muzzle velocity of the bullet is found by using the first equation of motion and by considering the initial velocity of bullet as zero.**

The muzzle velocity of ball is given as

\(v = u + at\)

Here, \(v\) is the muzzle velocity of bullet.

Substitute all the values in the above equation.

\(\begin{array}{l}v = 0 + \left( {6.20 \times {{10}^5}\;{\rm{m}}/{{\rm{s}}^2}} \right)\left( {8.10 \times {{10}^{ - 4}}\;{\rm{s}}} \right)\\v = 502.2\;{\rm{m}}/{\rm{s}}\end{array}\)

Therefore, the muzzle velocity of bullet is \(502.2\;{\rm{m}}/{\rm{s}}\).

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