To find the final speed after the collision where two cars stick together, we can use the principle of conservation of momentum.
The formula for momentum before and after the collision is:
\[ \text{Initial Momentum} = \text{Final Momentum} \]
The mass of the first car (m1) is 1300 kg and its initial velocity (v1) is 3.24 m/s. The second car (m2) has a mass of 1350 kg and is initially at rest (v2 = 0 m/s).
The initial momentum of the system before the collision is given by:
\[ \text{Initial Momentum} = m1 \cdot v1 + m2 \cdot v2 \] \[ = (1300 , \text{kg} \cdot 3.24 , \text{m/s}) + (1350 , \text{kg} \cdot 0 , \text{m/s}) \] \[ = 1300 \cdot 3.24 = 4212 , \text{kg m/s} \]
After the collision, the two cars stick together and move with a common velocity (v_f). The total mass after the collision (m_total) is:
\[ m_{\text{total}} = m1 + m2 = 1300 , \text{kg} + 1350 , \text{kg} = 2650 , \text{kg} \]
The final momentum (after the collision) is:
\[ \text{Final Momentum} = m_{\text{total}} \cdot v_f \]
Setting the initial momentum equal to the final momentum:
\[ 4212 , \text{kg m/s} = 2650 , \text{kg} \cdot v_f \]
To find \( v_f \), we can rearrange the equation:
\[ v_f = \frac{4212 , \text{kg m/s}}{2650 , \text{kg}} \] \[ v_f \approx 1.59 , \text{m/s} \]
Thus, the final speed of both cars moving forward after the collision is approximately 1.59 m/s.
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