A 1000 mathrm(~kg) car is traveling 12 mathrm(~m) / mathrm(s) to the right when it collides head-on with a 2000 mathrm(~kg) pickup truck traveling 8 mathrm(~m) / mathrm(s) to the left. The vehicles lock together inelastically following the collision. Which direction will the vehicles travel after the collision? left

## Step 1: Define the given values<br />### For the car:<br />- Mass, $m_1 = 1000 \, \text{kg}$<br />- Velocity, $v_1 = 12 \, \text{m/s}$ (to the right)<br /><br />### For the pickup truck:<br />- Mass, $m_2 = 2000 \, \text{kg}$<br />- Velocity, $v_2 = -8 \, \text{m/s}$ (to the left, hence negative)<br /><br />## Step 2: Calculate the initial momentum of each vehicle<br />### Momentum is calculated using the formula $p = m \cdot v$.<br /><br />### For the car:<br />\[<br />p_1 = m_1 \cdot v_1 = 1000 \, \text{kg} \cdot 12 \, \text{m/s} = 12000 \, \text{kg m/s}<br />\]<br /><br />### For the pickup truck:<br />\[<br />p_2 = m_2 \cdot v_2 = 2000 \, \text{kg} \cdot (-8) \, \text{m/s} = -16000 \, \text{kg m/s}<br />\]<br /><br />## Step 3: Calculate the total initial momentum<br />### The total initial momentum is the sum of the momenta of both vehicles.<br />\[<br />p_{\text{total}} = p_1 + p_2 = 12000 \, \text{kg m/s} + (-16000 \, \text{kg m/s}) = -4000 \, \text{kg m/s}<br />\]<br /><br />## Step 4: Determine the direction of travel after collision<br />### Since the total initial momentum is negative, the combined mass will move in the direction of the negative momentum, which is to the left.