To find the total momentum after the collision, we first need to calculate the total momentum before the collision.
In a closed system, the momentum before the collision is equal to the momentum after the collision due to the law of conservation of momentum.
Step 1: Calculate the momentum before the collision.
The momentum \( p \) of an object is given by the formula: \[ p = m \cdot v \] where:
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object.
In this case, we have two objects, each with a mass of \( 1.00 , \text{kg} \) moving toward each other at \( 1.80 , \text{m/s} \).
Let’s assign directions:
- Object 1 moving to the right: \( p_1 = 1.00 , \text{kg} \times 1.80 , \text{m/s} = 1.80 , \text{kg} \cdot \text{m/s} \)
- Object 2 moving to the left: \( p_2 = 1.00 , \text{kg} \times (-1.80 , \text{m/s}) = -1.80 , \text{kg} \cdot \text{m/s} \)
Step 2: Calculate the total momentum before the collision. \[ p_{\text{total}} = p_1 + p_2 = 1.80 , \text{kg} \cdot \text{m/s} - 1.80 , \text{kg} \cdot \text{m/s} = 0 , \text{kg} \cdot \text{m/s} \]
Step 3: Determine total momentum after the collision.
According to the conservation of momentum: \[ p_{\text{total, after}} = p_{\text{total, before}} = 0 , \text{kg} \cdot \text{m/s} \]
Therefore, the total momentum after the collision is 0 kg·m/s.