Answer:
Acceleration of the boy a₁:
[tex]a_{1} = 1.87 \frac{m}{s^{2} }[/tex]
Explanation:
Conceptual analysis
We apply Newton's second law to the boy and the girl:
F = m*a (Formula 1)
F : Force in Newtons (N)
m : mass in kilograms (kg)
a : acceleration in meters over second square (m/s²)
Nomenclature
m₁ : boy mass
m₂ : girl mass
a₁ : boy acceleration
a₂ : girl acceleration
F₁ : boy acceleration
F₂ : girl acceleration
Known data
m₁ = 57 kg
m₂ = 41 kg
a₂ = 2.6 m/s²
Problem development
We apply to Newton's third law of action and reaction, then:
F₁ = F₂ , We apply the formula (1):
m₁*a₁ = m₂*a₂
[tex]a_{1} = \frac{m_{2}* a_{2} }{m_{1} }[/tex]
[tex]a_{1} = \frac{41* 2.6 }{ 57 }[/tex]
[tex]a_{1} = 1.87 \frac{m}{s^{2} }[/tex]
