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## Homework Statement

A bullet has a mass of 7.5 g. It is fired into a ballistic pendulum. The pendulum's receiving block of wood is 2.5 kg. After the collision, the pendulum swings to a height of 0.1 m. What is the approximate velocity of the bullet?

[itex]m_{bullet} = 7.5g = 0.0075 kg[/itex]

[itex]m_{wood} = 2.5 kg[/itex]

[itex]h_i = 0 m[/itex]

[itex]h_f = 0.10 m[/itex]

[itex]g = 9.8 m/s^2[/itex]

## Homework Equations

[itex]KE_i + PE_i = KE_f + PE_f[/itex]

[itex]KE_i = \frac {1}{2}m_{bullet}v_{bullet}^2[/itex]

[itex]PE_i = 0[/itex]

[itex]KE_f = 0[/itex]

[itex]PE_f = (m_{bullet} + m_{block})gh_f[/itex]

## The Attempt at a Solution

[itex]KE_i + PE_i = KE_f + PE_f \Rightarrow \frac {1}{2}m_{bullet}v_{bullet}^2 + 0 = 0 + (m_{bullet} + m_{block})gh_f[/itex]

[itex]\Rightarrow \frac {1}{2}m_{bullet}v_{bullet}^2 = (m_{bullet} + m_{block})gh_f[/itex]

[itex]\Rightarrow v_{bullet} = \sqrt {\frac {2(m_{bullet} + m_{block})gh_f}{m_{bullet}}} = \sqrt {\frac {2((0.0075 kg) + (2.5 kg))(9.8 m/s^2)(0.10 m)}{(0.0075 kg)}}[/itex]

[itex]= 25.5986 \frac {m}{s} \sim 26 \frac {m}{s}[/itex]