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Two cars undergo a head-on collision. The first car has a mass of 1500 kg and was moving with a speed of 215 m/s. The second car has a mass of 1200 kg and was moving with a speed of 250 m/s. Find the direction and speed that the two cars will have right after the collision. (The collision can be considered as totally inelastic.)

Answer :

Final answer:

In a totally inelastic collision, two bodies stick together and move as a unit after the collision conserving the total initial momentum. By calculating the initial momentum of the cars, it was found that the combined mass moved at a speed of 8.33 m/s, in the same direction as the first car after the collision.

Explanation:

In totally inelastic collisions, the two objects stick together and move as a unit after the collision. The total momentum of the system is conserved, it remains the same before and after the collision, assuming no external forces act on the system such as friction.

First, let us find the initial momentum of each car:

  1. For the first car: p1 = m1 * v1 = 1500 kg * 215 m/s = 322500 kg.m/s
  2. For the second car, its velocity is given in opposite direction: p2 = m2 * -v2 = 1200 kg * -250 m/s = -300000 kg.m/s

Then, you find the total initial momentum: p_total_initial = p1 + p2 = 322500 kg.m/s - 300000 kg.m/s = 22500 kg.m/s.

Because total momentum is conserved, the final total momentum of the connected cars is also 22500 kg.m/s. As the mass is now combined (m_total = m1 + m2 = 1500 kg + 1200 kg = 2700 kg), you can find the speed by dividing the total momentum with the total mass: v_final = p_total_final/m_total = 22500 kg.m/s / 2700 kg = 8.33 m/s.

As p_total_initial is positive, the final velocity direction is the same as the direction of the first car.

Learn more about Inelastic Collision here:

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