Question

problem reference 7.2
at an intersection, a yellow subcompact car with mass 950 kg traveling east collides with a red truck with mass 1900 kg that is traveling north. the two vehicles stick together as a result of the of the collision, and the wreckage slides at 16.0 m/s in the direction 66.0° north of east. the collision occurs during a heavy rainstorm; ignore friction forces between the vehicles and the wet road.
what is the speed of the red truck before the collision?
9.76 m/s
21.9 m/s
43.8 m/s
24.0 m/s

Explanation:

Step1: Apply conservation of momentum in y - direction

The initial momentum of the car in y - direction is \(0\) (car is moving east). Let the mass of the car \(m_1 = 950\space kg\), mass of the truck \(m_2=1900\space kg\), final velocity \(v = 16.0\space m/s\) and the angle \(\theta = 66.0^{\circ}\).
The momentum after collision in y - direction is \((m_1 + m_2)v\sin\theta\). The initial momentum in y - direction is \(m_2u_2\) (where \(u_2\) is the initial velocity of the truck).
By conservation of momentum \(m_2u_2=(m_1 + m_2)v\sin\theta\)

Step2: Solve for \(u_2\)

Substitute \(m_1 = 950\space kg\), \(m_2 = 1900\space kg\), \(v = 16.0\space m/s\) and \(\theta = 66.0^{\circ}\) into the equation \(u_2=\frac{(m_1 + m_2)v\sin\theta}{m_2}\)

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Answer:

21.9 m/s