Question

there are two formulas I don't know which one it is
m1v1 + m2v2 = m1v1 + m2v2
m1v1 + m2v2 = (m1 + m2) vf

Tom is running at 6.0 m/s to the east. He collides with Jerry (mass = 84 kg), who was moving west at 4.0 m/s. Tom grabs hold of Jerry and the two move together at 0.72 m/s to the east. What is Tom’s mass?

Answer 1

Tom's mass is 75.1 kg

The law of conservation of momentum

This is the law of conservation of momentum which states that the initial and final momentum are the same.

The required equation

Since Tom grabs hold of Jerry after the colision, both stick together. So, we use the second equation.

m₁v₁ + m₂v₂ = (m₁ + m₂)vf where

• m₁ = Tom's mass,
• v₁ = Tom's velocity = + 6.0 m/s (since he is moving to the east),
• m₂ = Jerry's mass = 84 kg,
• v₂ = Jerry's velocity = -4.0 m/s (negative since he is moving to the west) and
• vf = their final velocity = 0.72 m/s

Since we require Jerry's mass, we make m₁ subject of the formula.

So, m₁v₁ + m₂v₂ = (m₁ + m₂)vf

m₁v₁ + m₂v₂ = m₁vf + m₂vf

m₁v₁ - m₁vf = m₂vf - m₂v₂

m₁(v₁ - vf) = m₂(vf - v₂)

The equation for Tom's mass

m₁ = m₂(vf - v₂)/(v₁ - vf)

Substituting the values of the variables into the equation, we have

m₁ = m₂(vf - v₂)/(v₁ - vf)

m₁ = 84 kg(0.72 m/s - [-4.0 m/s])/(6.0 m/s - 0.72 m/s)

m₁ = 84 kg(0.72 m/s + 4.0 m/s)/(6.0 m/s - 0.72 m/s)

m₁ = 84 kg(4.72 m/s)/(5.28 m/s)

m₁ = 396.48 kgm/s ÷ 5.28 m/s

m₁ = 75.09 kg

m₁ ≅ 75.1 kg

So, Tom's mass is 75.1 kg

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