Use the law of conservation of momentum to relate the velocity V' of the block (with embedded bullet) after impact, and the velocity of the bullet before impact, V.
0.00795 V = (9.03 + 0.0008)*V'
You already know V'. Solve for V.
0.00795 V = (9.03 + 0.0008)*V'
You already know V'. Solve for V.
The momentum of an object is calculated by multiplying its mass by its velocity. In this case, we need to calculate the momentum of the bullet before the collision and the momentum of the block and bullet together after the collision.
Let's use the following variables:
- m_bullet: mass of the bullet
- v_bullet: initial velocity of the bullet
- m_block: mass of the wood block
- v_final: final velocity of the block and bullet together after the collision
Given information:
- m_bullet = 7.95 g = 0.00795 kg
- m_block = 9.03 kg
- v_final = 11.6 cm/s = 0.116 m/s
Now we can apply the conservation of momentum principle:
Initial momentum = Final momentum
m_bullet * v_bullet = (m_bullet + m_block) * v_final
Substituting the given values:
0.00795 kg * v_bullet = (0.00795 kg + 9.03 kg) * 0.116 m/s
Simplifying the equation:
v_bullet = ((0.00795 kg + 9.03 kg) * 0.116 m/s) / 0.00795 kg
v_bullet = (9.03895 kg * 0.116 m/s) / 0.00795 kg
v_bullet ≈ 0.131 m/s
Therefore, the initial speed of the bullet was approximately 0.131 m/s.