Respuesta :
Explanation:
The given data is as follows.
Mass of bullet 1, [tex]m_{b}[/tex] = 7 g = [tex]7 \times 10^{-3} kg[/tex]
Mass of block of wood, M = 1.10 kg
Bullet penetrates to depth, [tex]x_{1}[/tex] = 9.60 cm = [tex]9.60 \times 10^{-2} m[/tex]
Mass of bullet 2, [tex]m_{B}[/tex] = 7 g = [tex]7 \times 10^{-3} kg[/tex]
Velocity of bullet = v
Let us assume that depth of penetration of the bullet is [tex]x_{2}[/tex].
According to the law of conservation of energy,
Kinetic energy = Potential energy
Kinetic energy = [tex]\frac{1}{2}mv^{2}[/tex]
and, Potential energy = mgh
so, for bullet 1
[tex]\frac{1}{2}m_{b}v^{2}_{1} = m_{b}gx_{1}[/tex] .......... (1)
For bullet 2,
Kinetic energy of bullet 1 - kinetic energy of bullet 2 = Potential energy
[tex]\frac{1}{2}m_{b}v^{2}_{1} - \frac{1}{2}(M + m_{b} + m_{B})v^{2}_{2} = m_{b}gx_{2}[/tex]
Using equation (1), we get
[tex]m_{b}gx_{1} - \frac{1}{2}(M + m_{b} + m_{B})v^{2}_{2} = m_{b}gx_{2}[/tex]
[tex]x_{2} = \frac{x_{1}(M + m_{b})}{(M + m_{b} + m_{B})}[/tex]
Putting the given values into the above formula as follows.
[tex]x_{2} = \frac{x_{1}(M + m_{b})}{(M + m_{b} + m_{B})}[/tex]
= [tex]\frac{9.60 \times 10^{-2}(1.10 + 7 \times 10^{-3})}{(1.10 + 7 \times 10^{-3} + 7 \times 10^{-3})}[/tex]
= 0.0953 m
or, = 9.53 cm (as 1 m = 100 cm)
Thus, we can conclude that the bullet will penetrate at a depth of 9.53 cm.
