A 14 g ball of clay traveling east at 3.4 m/s collides with a 30 g ball of clay

Question

A 14 g ball of clay traveling east at 3.4 m/s collides with a 30 g ball of clay traveling north at 2.0 m/s. What are the speed and the direction of the resulting 44 g ball of clay? Three identical train cars, coupled together, are rolling east at 1.6 m/s. A fourth car traveling east at 4.6 m/s catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?

Explanation / Answer

Momentum conservation

Part1.

Assuming X axis as east and Y axis as north .

Initial momentum In vector form = 14×3.4 i + 30×2 j = 47.6 i + 60j

Final momentum = 44×V

Initial = final

Or. 44V =47.6 i + 60 j

Or. V = 1.08 i + 1.36 j m/s

Hence speed = 1.74 m/s

Angle = 51.55

Hence 51.55° north of east.

Part2.

Initial momentuml= final momentum

3m×1.6 + m×4.6 = 5m ×V

Or. V = 1.88 m/s

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