An incoming meteor with mass 65.4 kg and velocity \( +12.46 \mathrm{~km} / \mathrm{s} \) overtakes another meteor with mass 32.1 kg and velocity \( +8.56 \mathrm{~km} / \mathrm{s} \). The two meteors stick together. What is their velocity?

To find the final velocity of the two meteors after they collide and stick together, we can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision. The momentum for each meteor is given by the formula: \[ \text{Momentum} = \text{mass} \times \text{velocity} \] Calculating the momentum of each meteor: 1. For the first meteor: \( p_1 = 65.4 \, \text{kg} \times 12.46 \, \text{km/s} = 815.964 \, \text{kg km/s} \) 2. For the second meteor: \( p_2 = 32.1 \, \text{kg} \times 8.56 \, \text{km/s} = 274.776 \, \text{kg km/s} \) Total momentum before the collision: \[ p_{total} = p_1 + p_2 = 815.964 \, \text{kg km/s} + 274.776 \, \text{kg km/s} = 1090.74 \, \text{kg km/s} \] Since the two meteors stick together after the collision, the combined mass \( m_{total} = 65.4 \, \text{kg} + 32.1 \, \text{kg} = 97.5 \, \text{kg} \). Using the conservation of momentum to find the final velocity \( v_f \): \[ p_{total} = m_{total} \times v_f \] \[ 1090.74 \, \text{kg km/s} = 97.5 \, \text{kg} \times v_f \] \[ v_f = \frac{1090.74 \, \text{kg km/s}}{97.5 \, \text{kg}} \approx 11.16 \, \text{km/s} \] Therefore, the final velocity of the two meteors stuck together is approximately \( 11.16 \, \text{km/s} \).