Questions: A 1500-kg car moving at 15 m/s collided head-on with a 2000-kg SUV traveling at -20 m/s. If the car now moves at -1 m/s, what is the new speed of the SUV?

Solution Steps

• The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces act on the system.

• Calculate the initial momentum of the car: \[ p_{\text{car, initial}} = m_{\text{car}} \times v_{\text{car, initial}} = 1500 \, \text{kg} \times 15 \, \text{m/s} = 22500 \, \text{kg} \cdot \text{m/s} \]
• Calculate the initial momentum of the SUV: \[ p_{\text{SUV, initial}} = m_{\text{SUV}} \times v_{\text{SUV, initial}} = 2000 \, \text{kg} \times (-20) \, \text{m/s} = -40000 \, \text{kg} \cdot \text{m/s} \]
• Calculate the total initial momentum: \[ p_{\text{total, initial}} = p_{\text{car, initial}} + p_{\text{SUV, initial}} = 22500 \, \text{kg} \cdot \text{m/s} - 40000 \, \text{kg} \cdot \text{m/s} = -17500 \, \text{kg} \cdot \text{m/s} \]

• Calculate the final momentum of the car: \[ p_{\text{car, final}} = m_{\text{car}} \times v_{\text{car, final}} = 1500 \, \text{kg} \times (-1) \, \text{m/s} = -1500 \, \text{kg} \cdot \text{m/s} \]
• Use the conservation of momentum to find the final momentum of the SUV: \[ p_{\text{total, final}} = p_{\text{total, initial}} = -17500 \, \text{kg} \cdot \text{m/s} \] \[ p_{\text{SUV, final}} = p_{\text{total, final}} - p_{\text{car, final}} = -17500 \, \text{kg} \cdot \text{m/s} - (-1500 \, \text{kg} \cdot \text{m/s}) = -16000 \, \text{kg} \cdot \text{m/s} \]

• Use the final momentum of the SUV to find its final speed: \[ v_{\text{SUV, final}} = \frac{p_{\text{SUV, final}}}{m_{\text{SUV}}} = \frac{-16000 \, \text{kg} \cdot \text{m/s}}{2000 \, \text{kg}} = -8 \, \text{m/s} \]

Final Answer