Question

1. a 1500 - kg truck moving west at 39.1 m/s collides with a 855 - kg car moving east at 10.4 m/s. after the collision, the two cars are stuck together. with what speed do they move after the collision? define the system as the two cars.

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that \(p_{initial}=p_{final}\). The initial momentum is the sum of the momenta of the truck and the car. Let the west - east direction be the \(x\) - axis. The mass of the truck \(m_1 = 1500\space kg\), its velocity \(v_1=- 39.1\space m/s\) (negative because it moves west), the mass of the car \(m_2 = 855\space kg\), its velocity \(v_2 = 10.4\space m/s\). The final mass \(m=m_1 + m_2=(1500 + 855)\space kg=2355\space kg\), and the final velocity is \(v\).

The initial momentum \(p_{initial}=m_1v_1+m_2v_2\), and the final momentum \(p_{final}=(m_1 + m_2)v\). So, \(m_1v_1+m_2v_2=(m_1 + m_2)v\)

Step2: Substitute the values into the formula

Substitute \(m_1 = 1500\space kg\), \(v_1=-39.1\space m/s\), \(m_2 = 855\space kg\), \(v_2 = 10.4\space m/s\) into the equation \(v=\frac{m_1v_1+m_2v_2}{m_1 + m_2}\)

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Answer:

-21.13 m/s