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Sheila weighs 60 kg and is riding a bike. Her momentum on the bike is 340 kg . m/s. The bike hits a rock, which stops it
completely and throws Sheila forward onto the pavement
If there is no net force on the system, what is Sheila's velocity immediately after she is thrown from the bike?
1.8 m/s
2.0 m/s
5.0 m/s
5.7 m/s
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The correct answer is 5.7

Explanation:

1) Physical principle: conservation of momentum.

If there is not net external force acting on a systmen, then the total momentum of the system is conserved.The momentum, p, is a vectorial magnitude defined as the product of the mass by the velocity: p = mv.

2) In consequence, considering that there is no net force on the system, Sheila and the bike’s momentum before and after the collision is the same.

So, now do the calculations:

Momentum before the collision:

        p₁ = (mass of Sheila + mass of the bike)×velocity

        p₁ = (60kg + m) × v₁ = 340 kg • m/s

Momentum after collision:

       p₂ = mass of sheila × velocity of Sheila + mass of the bike × velocity of the bike

       p₂ = 60kg × v₂ + m×0 = 60kg × v₂

       p₁ = p₂ ⇒ (60kg + m) × v₁ = 60kg × v₂ ⇒ 340 kg • m/s = 60kg × v₂

       ⇒ v₂ = 340 kg • m/s / 60 kg ≈ 5.7 m/s ← answer

Final reflection: since the momentum is conserved and the bike stops completely after the collision, Sheila wil keep the total momentum, and you can calculate her velocity dividing the total momentum by her mass:  v = 340 kg • m/s / 60 kg ≈ 5.7 m/s

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