In a target shooting game, wooden blocks are thrown into the air and shot in flight. A block of 0.8kg has a speed of 10 m/s at the top of its trajectory when it is hit by a bullet from below at an angel 60° from horizontal. The mass of the bullet is 5.0 g and its speed is 550m/s when it hits the block. The bullet is embedded in the block. What is the velocity of the block immediately after impact?
To find the velocity of the block immediately after impact, we need to apply the principle of conservation of linear momentum. According to this principle, the total momentum before the impact is equal to the total momentum after the impact.
1. Convert the mass of the bullet from grams to kilograms:
The mass of the bullet is given as 5.0 g. Since 1 kg = 1000 g, the mass of the bullet in kilograms is:
5.0 g / 1000 = 0.005 kg
2. Calculate the initial momentum of the bullet:
Momentum (P) is calculated by multiplying mass (m) by velocity (v):
Momentum of the bullet before impact (P_bullet) = Mass of the bullet (m_bullet) × Velocity of the bullet (v_bullet)
P_bullet = 0.005 kg × 550 m/s
3. Calculate the initial momentum of the wooden block:
The velocity of the wooden block just before impact is given as 10 m/s. Since the block is only moving vertically at the top of its trajectory, its horizontal velocity component is zero. Therefore, only the vertical component of the velocity contributes to the momentum.
Momentum of the wooden block before impact (P_block) = Mass of the block (m_block) × Vertical Velocity of the block (v_block)
P_block = 0.8 kg × 10 m/s
4. To calculate the total momentum before impact, we need to consider both the bullet and the block:
Total momentum before impact = P_bullet + P_block
5. After the impact, the bullet becomes embedded in the block. Since they are now moving together, we can consider them as a single combined mass.
6. Let the velocity of the block and bullet combination after impact be V_final.
The mass of the block and bullet combination after impact is the sum of their masses:
Mass after impact (m_combined) = mass of the block (m_block) + mass of the bullet (m_bullet)
7. Since momentum is conserved, we can equate the total momentum before impact to the momentum after impact:
Total momentum before impact = Total momentum after impact
P_bullet + P_block = m_combined × V_final
8. Solve for V_final to determine the velocity of the block immediately after impact.
By following these steps, you should be able to calculate the velocity of the block immediately after the impact.