A 30g bullet with a speed of 400m=s strikes a glancing blow to a
target brick of mass 1:0kg. The Brick breaks into two fragments.
The bullet deflects at a angle of 30� above the +x-axis and has a
reduced speed of 100m=s. One piece of the brick with mass
(0.75kg) goes off to the right with a speed of 5:0m=s. Determine
the speed and direction of the other piece of the brick immediately
after the collison.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after a collision.
1. Calculate the initial momentum of the bullet before the collision:
- Mass of the bullet (m1) = 30g = 0.03kg
- Initial velocity of the bullet (v1) = 400m/s
- Initial momentum of the bullet (P1) = m1 * v1
2. Calculate the initial momentum of the brick before the collision:
- Mass of the brick (m2) = 1.0kg
- Initial velocity of the brick (v2) = 0 (since the brick is initially at rest)
- Initial momentum of the brick (P2) = m2 * v2
3. Calculate the final momentum of the bullet after the collision:
- Final velocity of the bullet (v1f) = 100m/s (given)
- Angle of deflection (θ) = 30 degrees (given)
- Final momentum of the bullet (P1f) = m1 * v1f
4. Determine the momentum of the other piece of the brick:
- Let the mass of the other piece of the brick be m3
- Let the velocity of the other piece of the brick be v3
5. Use the conservation of momentum principle to create an equation:
- Initial momentum before the collision (P1 + P2) = Final momentum after the collision (P1f + P3)
- (m1 * v1) + (m2 * v2) = (m1 * v1f) + (m3 * v3)
6. Rearrange the equation to solve for v3:
- v3 = [(m1 * v1) + (m2 * v2) - (m1 * v1f)] / m3
7. Calculate the final velocity of the other piece of the brick (v3):
- Substitute the known values into the equation:
- v3 = [(0.03kg * 400m/s) + (1.0kg * 0m/s) - (0.03kg * 100m/s)] / 0.75kg
8. Calculate the result:
- v3 = [12 + 0 - 3] / 0.75 = 9 m/s
Therefore, the other piece of the brick moves in the opposite direction of the bullet with a speed of 9m/s after the collision.