A 900kg car, traveling 13m/s to the right collides with a 3000kg semi truck initially at rest. After the 0.7s collision, the semi truck ends up moving 5.3m/s right. vert Jvert =15,900kgm/s before collision: P_(car)=11,700kgm/s P_(truck)=0 kgm/s after collision: P_(car)=square kgm/s P_(truck)=15,900kgm/s What direction did the car move after the collision? square v How fast did the car move after the collision? square m/s

To solve this problem, we will use the **law of conservation of momentum** and the given data. The total momentum before the collision must equal the total momentum after the collision.<br /><br />---<br /><br />### Step 1: Write down the known values<br />- Mass of the car (\(m_{\text{car}}\)) = \(900 \, \mathrm{kg}\)<br />- Initial velocity of the car (\(v_{\text{car, initial}}\)) = \(13 \, \mathrm{m/s}\) (to the right)<br />- Mass of the truck (\(m_{\text{truck}}\)) = \(3000 \, \mathrm{kg}\)<br />- Initial velocity of the truck (\(v_{\text{truck, initial}}\)) = \(0 \, \mathrm{m/s}\) (at rest)<br />- Final velocity of the truck (\(v_{\text{truck, final}}\)) = \(5.3 \, \mathrm{m/s}\) (to the right)<br /><br />The impulse on the truck is given as:<br />\[<br />|\mathrm{J}| = 15,900 \, \mathrm{kg} \cdot \mathrm{m/s}<br />\]<br /><br />---<br /><br />### Step 2: Calculate the total momentum before the collision<br />The total momentum before the collision is the sum of the momenta of the car and the truck:<br />\[<br />P_{\text{total, before}} = P_{\text{car, before}} + P_{\text{truck, before}}<br />\]<br />\[<br />P_{\text{car, before}} = m_{\text{car}} \cdot v_{\text{car, initial}} = 900 \cdot 13 = 11,700 \, \mathrm{kg} \cdot \mathrm{m/s}<br />\]<br />\[<br />P_{\text{truck, before}} = m_{\text{truck}} \cdot v_{\text{truck, initial}} = 3000 \cdot 0 = 0 \, \mathrm{kg} \cdot \mathrm{m/s}<br />\]<br />\[<br />P_{\text{total, before}} = 11,700 + 0 = 11,700 \, \mathrm{kg} \cdot \mathrm{m/s}<br />\]<br /><br />---<br /><br />### Step 3: Calculate the total momentum after the collision<br />The total momentum after the collision is the sum of the momenta of the car and the truck:<br />\[<br />P_{\text{total, after}} = P_{\text{car, after}} + P_{\text{truck, after}}<br />\]<br />We know the momentum of the truck after the collision:<br />\[<br />P_{\text{truck, after}} = m_{\text{truck}} \cdot v_{\text{truck, final}} = 3000 \cdot 5.3 = 15,900 \, \mathrm{kg} \cdot \mathrm{m/s}<br />\]<br />Using the law of conservation of momentum:<br />\[<br />P_{\text{total, before}} = P_{\text{total, after}}<br />\]<br />\[<br />11,700 = P_{\text{car, after}} + 15,900<br />\]<br />Solve for \(P_{\text{car, after}}\):<br />\[<br />P_{\text{car, after}} = 11,700 - 15,900 = -4,200 \, \mathrm{kg} \cdot \mathrm{m/s}<br />\]<br /><br />---<br /><br />### Step 4: Determine the direction of the car's motion after the collision<br />The negative sign in \(P_{\text{car, after}} = -4,200 \, \mathrm{kg} \cdot \mathrm{m/s}\) indicates that the car is moving to the **left** after the collision.<br /><br />---<br /><br />### Step 5: Calculate the car's velocity after the collision<br />The momentum of the car after the collision is related to its velocity by:<br />\[<br />P_{\text{car, after}} = m_{\text{car}} \cdot v_{\text{car, after}}<br />\]<br />Substitute the known values:<br />\[<br />-4,200 = 900 \cdot v_{\text{car, after}}<br />\]<br />Solve for \(v_{\text{car, after}}\):<br />\[<br />v_{\text{car, after}} = \frac{-4,200}{900} = -4.67 \, \mathrm{m/s}<br />\]<br /><br />The negative sign confirms that the car is moving to the **left**, and its speed is:<br />\[<br />v_{\text{car, after}} = 4.67 \, \mathrm{m/s}<br />\]<br /><br />---<br /><br />### Final Answers:<br />1. **Direction of the car after the collision:** Left<br />2. **Speed of the car after the collision:** \(4.67 \, \mathrm{m/s}\)