Question

Two football players with mass 120 kg and 90 kg run directly toward each other with speeds 8 m/s and 5 m/s respectively. After they collide, the larger player continues forward with a speed of 2 m/s. What is the new speed of the second player?

Answer 1

The new speed of the second player just after the collision is 13m/s.

Conservation of momentum

The Law of Conservation of Momentum simply states that the total momentum of an isolated system remains constant. that is to say;

Initial momentum = Final momentum

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Given the data in the question;

• Mass of larger player m₁ = 120kg

• Mass of smaller player m₂ = 90kg

• Velocity of larger player before collision u₁ = 8m/s

• Velocity of smaller player before collision u₂ = 5m/s

• Velocity of larger player after collision v₁ = 2m/s

• Velocity of smaller player after collision v₂ = ?

To determine the speed of the smaller player after the collision, we substitute our given values into the expression above.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(120kg × 8m/s) + (90kg × 5m/s) = (120kg × 2m/s) + (90kg × v₂)

960kgm/s + 450kgm/s = 240kgm/s + (90kg × v₂)
1410kgm/s = 240kgm/s + (90kg × v₂)

(90kg × v₂) = 1410kgm/s  -  240kgm/s

90kg × v₂ = 1170kgm/s

v₂ = 1170kgm/s ÷ 90kg

v₂ = 13m/s

Therefore, the new speed of the second player just after the collision is 13m/s.

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