Answer:
The child's mass is 14.133 kg
Explanation:
From the principle of conservation of linear momentum, we have;
(m₁ + m₂) × v₁ + m₃ × v₂ = (m₁ + m₂) × v₃ - m₃ × v₄
We include the negative sign as the velocities were given as moving in the opposite directions
Since the child and the ball are at rest, we have;
v₁ = 0 m/s and v₂= 0 m/s
Hence;
0 = m₁ × v₃ - m₂ × v₄
(m₁ + m₂)× v₃ = m₃ × v₄
Where:
m₁ = Mass of the child
m₂ = Mass of the scooter = 2.4 kg
v₃ = Final velocity of the child and scooter = 0.45 m/s
m₃ = Mass of the ball = 2.4 kg
v₄ = Final velocity of the ball = 3.1 m/s
Plugging the values gives;
(m₁ + 2.4)× 0.45 = 2.4 × 3.1
(m₁ + 2.4) = 16.533
∴ m₁ + 2.4 = 16.533
m₁ = 16.533 - 2.4 = 14.133 kg
The child's mass = 14.133 kg.
