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If a 2,199 kg car traveling at 32 km/h collides with a 4,181 kg car that is stationary (0 m/s), how fast are they moving after the collision? (Use the collision equation.) Round to the nearest tenth.

Answer :

Final answer:

After the collision of a 2,199 kg car traveling at 32 km/h with a 4,181 kg stationary car, both cars would be moving together at a speed of 3.1 m/s, calculated using the conservation of momentum.

Explanation:

If a 2,199 kg car going 32 km/h hits a 4,181 kg car waiting at a stop light (0 m/s), we can find how fast they are moving after the collision by using the law of conservation of momentum. This law states that, in the absence of external forces, the total momentum before the collision is equal to the total momentum after the collision.

Since the second car is at rest before the collision, its initial momentum is zero. The first car's initial momentum can be calculated by multiplying its mass by its velocity (which we need to convert from km/h to m/s by dividing by 3.6). Once we have the total initial momentum, we divide it by the combined mass of both cars to find their common velocity after the collision.

Here are the calculations:

  • Initial momentum of first car: mass × velocity = 2199 kg × (32 km/h / 3.6) = 2199 kg × 8.89 m/s = 19549.11 kg·m/s
  • Combined mass of both cars: 2199 kg + 4181 kg = 6380 kg
  • Velocity after collision: total momentum / combined mass = 19549.11 kg·m/s / 6380 kg = 3.0639 m/s

After rounding to the nearest tenth, the two cars would be moving at 3.1 m/s after the collision.

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