Let’s solve each problem step by step.
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Problem 1:
Two trains (one freight, one passenger) collide and couple. Find final velocity.
Given:
- Freight train: mass = 5000 kg, velocity = +2 m/s (let’s say to the right is positive)
- Passenger train: mass = 3000 kg, velocity = -4 m/s (to the left)
They stick together → inelastic collision → use conservation of momentum.
Total initial momentum = total final momentum
Initial momentum:
= (mass_freight × velocity_freight) + (mass_passenger × velocity_passenger)
= (5000 × 2) + (3000 × (-4))
= 10,000 – 12,000
=
-2000 kg·m/s
Final combined mass = 5000 + 3000 =
8000 kg
Let final velocity = v
So:
8000 × v = -2000
→ v = -2000 / 8000 =
-0.25 m/s
Negative means they move to the left after collision.
✔ Final Answer for Problem 1:
-0.25 m/s
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Problem 2:
A 2 kg object moving at 6 m/s hits a stationary 4 kg object. After collision, first object moves at 2 m/s. What’s speed of second object?
This is also conservation of momentum.
Initial momentum:
= (2 kg × 6 m/s) + (4 kg × 0 m/s) =
12 kg·m/s
After collision:
First object: 2 kg × 2 m/s = 4 kg·m/s
Second object: let its velocity be v → 4 kg × v
Total final momentum = 4 + 4v
Set equal to initial:
4 + 4v = 12
→ 4v = 8
→ v =
2 m/s
✔ Final Answer for Problem 2:
2 m/s
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Problem 3:
Football player (80 kg) running at 5 m/s tackles referee (70 kg) standing still. They fall together. What’s their velocity?
Again, conservation of momentum — inelastic collision.
Initial momentum:
= (80 × 5) + (70 × 0) =
400 kg·m/s
Combined mass = 80 + 70 =
150 kg
Final velocity = v
150 × v = 400
→ v = 400 / 150 ≈
2.666... m/s
We can write as fraction: 400 ÷ 150 = 8/3 ≈
2.67 m/s (rounded to two decimals)
But since the problem says “round to nearest tenth”, we do:
400 ÷ 150 = 2.666... → rounds to
2.7 m/s
Wait — let me check rounding rule:
2.666... → look at hundredths place (6), which is ≥5 → round up tenths place from 6 to 7 → yes,
2.7 m/s
✔ Final Answer for Problem 3:
2.7 m/s
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Final Answer:
Problem 1: -0.25 m/s
Problem 2: 2 m/s
Problem 3: 2.7 m/s
Parent Tip: Review the logic above to help your child master the concept of conservation of momentum worksheet.
