Answer:
[tex]F = 22298.824\,N[/tex]
Explanation:
According to the Principle of Energy Conservation and the Work-Energy Theorem, the bullet has the following expression:
[tex]U_{g,A} + K_{A} = U_{g,B} + K_{B} + W_{loss}[/tex]
[tex]W_{loss} = U_{g,A}-U_{g,B} + K_{A}-K_{B}[/tex]
[tex]F\cdot \Delta s = \frac{1}{2}\cdot m \cdot [v_{A}^{2}-v_{B}^{2}][/tex]
The average force exerted on the bullet to stop it is:
[tex]F = \frac{m\cdot [v_{A}^{2}-v_{B}^{2}]}{2\cdot \Delta s}[/tex]
[tex]F = \frac{(7.8\times 10^{-3}\,kg)\cdot [(540\,\frac{m}{s} )^{2}-(0\,\frac{m}{s} )^{2}]}{2\cdot (0.051\,m)}[/tex]
[tex]F = 22298.824\,N[/tex]
