Cart X (mass ) moves east at and collides with Cart Y (mass ) moving west at

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Cart X (mass 1.0 kg1.0\,\text{kg}) moves east at 4.0 m s−14.0\,\text{m\,s}^{-1} and collides with Cart Y (mass 2.0 kg2.0\,\text{kg}) moving west at 1.0 m s−11.0\,\text{m\,s}^{-1}. The two carts stick together. Immediately afterward, a third cart Z (mass 1.5 kg1.5\,\text{kg}) is to be gently coupled to the combined pair so that the final three-cart system has zero center-of-mass velocity. What velocity (magnitude and direction, with east taken as positive) must cart Z have just before coupling?

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