Block $$ 1(3.00 \mathrm{~kg}) $$ is moving right at $$ 2.09 \mathrm{~m} / \mathrm{s} $$ Block $$ 2(2.22 \mathrm{~kg}) $$ is moving left at $$ 3.92 \mathrm{~m} / \mathrm{s} $$. Block 1 collides with block 2 . Afterwards block 1 moves left at $$ 1.71 \mathrm{~m} / \mathrm{s} $$. What is the final velocity of block 2 after the collision? $$ v_{2 f}=[?] \mathrm{m} / \mathrm{s} $$ Remember to indicate if the velocity is to the right ( + or to the left ( - )

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To find the final velocity of block 2 after the collision, we can use the principle of conservation of momentum.

Given:
- Mass of block 1: $$ m_1 = 3.00 \, \text{kg} $$
- Initial velocity of block 1: $$ v_{1i} = 2.09 \, \text{m/s} $$ to the right
- Mass of block 2: $$ m_2 = 2.22 \, \text{kg} $$
- Initial velocity of block 2: $$ v_{2i} = -3.92 \, \text{m/s} $$ to the left
- Final velocity of block 1: $$ v_{1f} = -1.71 \, \text{m/s} $$ to the left

We can use the formula for conservation of momentum:
$$ m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f} $$

Substitute the given values into the formula:
$$ 3.00 \times 2.09 + 2.22 \times (-3.92) = 3.00 \times (-1.71) + 2.22 \times v_{2f} $$

Solve for $$ v_{2f} $$:
$$ 6.27 - 8.69 = -5.13 + 2.22 \times v_{2f} $$
$$ -2.42 = -5.13 + 2.22 \times v_{2f} $$
$$ 2.22 \times v_{2f} = 2.71 $$
$$ v_{2f} = \frac{2.71}{2.22} $$

Calculate the final velocity of block 2 after the collision.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2.71}{2.22}$$
- step1: Convert the expressions:
  $$\frac{\frac{271}{100}}{\frac{111}{50}}$$
- step2: Multiply by the reciprocal:
  $$\frac{271}{100}\times \frac{50}{111}$$
- step3: Reduce the numbers:
  $$\frac{271}{2}\times \frac{1}{111}$$
- step4: Multiply the fractions:
  $$\frac{271}{2\times 111}$$
- step5: Multiply:
  $$\frac{271}{222}$$
The final velocity of block 2 after the collision is $$ v_{2f} = 1.2\dot{2}0\dot{7} \, \text{m/s} $$ to the right.
The final velocity of block 2 after the collision is $$ 1.22 \, \text{m/s} $$ to the right.

Block is moving right at
Block is moving left at .
Block 1 collides with block 2 . Afterwards
block 1 moves left at .
What is the final velocity of block 2
after the collision?

Remember to indicate if the velocity
is to the right ( + or to the left ( - )

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Block is moving right at Block is moving left at . Block 1 collides with block 2 . Afterwards block 1 moves left at . What is the final velocity of block 2 after the collision? Remember to indicate if the velocity is to the right ( + or to the left ( - )