A 1200 kg car travels east at 15 m/s. It collides head-on with a 900 kg van travelling west at 20 m/s. The vehicles lock together after the collision. The d...
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A 1200 kg car travels east at 15 m/s. It collides head-on with a 900 kg van travelling west at 20 m/s. The vehicles lock together after the collision. The diagram shows the directions.
In which direction and at what speed do the locked vehicles move after the collision?
Answer Details
This is a head-on collision where two vehicles travelling in opposite directions lock together. The key is to assign a positive direction and apply conservation of momentum.
Taking east as positive:
\[ p_{\text{total}} = m_{\text{car}} \times v_{\text{car}} + m_{\text{van}} \times v_{\text{van}} \]
The car's momentum is \( 1200 \times 15 = 18\,000 \text{ kg m/s} \) (east), and the van's momentum is \( 900 \times (-20) \) (west, so negative). Since the vehicles lock together, the combined mass is \( 1200 + 900 = 2100 \text{ kg} \).
\[ v = \frac{p_{\text{total}}}{m_{\text{total}}} \]
Substituting gives a small positive velocity, meaning the locked vehicles move east. The result is approximately 0.71 m/s, confirming the direction is east. When two objects collide head-on with nearly equal momenta, the combined object moves slowly in the direction of whichever had the slightly greater momentum.
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