An 800 kg car moving at 80 km hr ^ -1 collides with a 1200 kg car moving at 40 km hr ^ -1 in the same…

Analyze the question: Two cars move in the same direction and stick together after the collision. This is a perfectly inelastic collision, so momentum is conserved.

Concept: Total momentum before = total momentum after

m₁u₁ + m₂u₂ = (m₁ + m₂)v

Since the cars are moving in the same direction, both momenta are positive. We can keep the speeds in km/hr because the units cancel in the final ratio.

Solution:

• Momentum of the first car: 800 × 80 = 64,000
• Momentum of the second car: 1200 × 40 = 48,000
• Total momentum: 64,000 + 48,000 = 112,000
• Total mass: 800 + 1200 = 2000 kg

v = 112,000 / 2000 = 56 km/hr

Check: The common velocity must lie between 40 and 80 km/hr. 56 does, and it is closer to 40 because the 1200 kg car is heavier.

Answer: D. 56 km hr⁻¹

Tip: For "stick together" problems, use m₁u₁ + m₂u₂ = (m₁ + m₂)v. If the cars move in opposite directions, give one velocity a negative sign. You can also quickly check that your answer lies between the two initial speeds. That helps you rule out options like B (8) and A (60, which is too high for a weighted average pulled toward 40).