9)A 64 kg parent and a 16 kg child meet at the center of an ice rink. They place their hands together and push. (A) Is the force experienced by the child more than, less than, or the same as the force experienced by the parent? (B) is the
acceleration of the child more than, less than, or the same as the acceleration of the parent? Explain. (C) If the
acceleration of the child is 2.5 m/s^2 in magnitude, what is the magnitude of the parent's acceleration?

(A) The same

(B) More

(C) The magnitude of the parent's acceleration is 0.625 m/s²

Explanation:

The given parameters are;

The mass of the parent, m₁ = 64 kg

The mass of the child, m₂ = 16 kg

(A) By Newton's third law of motion, action and reaction are equal and opposite

Therefore, the action of the parent on the child is equal to the reaction of the child on the parent and vice versa

Therefore, the force experienced by the child is the same as the force experienced by the parent

(B) Newton's second law states that an objects acceleration is directly proportional to the applied force and inversely proportional to the mass of the object

Therefore, the parent and the child both experience the same force but the mass of the child is less than the mass of the parent and therefore, by Newton's second law, the acceleration of the child will be more than the acceleration of the parent for the same given force

(C) The acceleration of the child, a₂ = 2.5 m/s²

Let F₁ represent the force experienced by the parent, let F₂ represent the force experienced by the child and let a₁ represent the magnitude of the parent's acceleration

By Newton's third law, we have;

F₁ = F₂

Force, F = Mass, m × Acceleration, a

We can write, F = m × a

Therefore;

F₁ = m₁ × a₁ and F₂ = m₂ × a₂

∴ F₁ = F₂ gives;

m₁ × a₁ = m₂ × a₂

a₁ = (m₂ × a₂)/m₁ = (16 × 2.5)/64 = 0.625

∴ The magnitude of the parent's acceleration = a₁ = 0.625 m/s²