Suppose a 63-kg boy and a 40-kg girl use a massless rope in a tug-of-war on an icy, resistance-free surface. if the acceleration of the girl toward the boy is 3.0 m/s2, find the magnitude of the acceleration of the boy toward the girl.

a₂ = 1.9 m/s²

Explanation:

Newton's third law or principle of action and reaction :

Force of the boy on the girl = -  Force of the girl on the boy

Fbg = - Fgb  Formula (1)

Newton's second law

∑F = m*a Formula (2)

∑F : algebraic sum of the forces in Newton (N)  

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Newton's second law to the girl

m₁ : girl mass

a₁ : acceleration of the girl toward the boy

∑F = m₁*a₁

Fbg= (40kg)*(3 m/s²)

Fbg = 120 N

Newton's second law to the boy

m₂: boy mass

a₂ : acceleration of the boy toward the girl

∑F = m₂*a₂

Fgb = (63)*a₂

120 = (63)*a₂

a₂ = 120 / (63)

a₂ = 1.9 m/s²

the arctic is a region of the planet, north of the arctic circle, and includes the arctic ocean, greenland, baffin island, other smaller northern islands, and the far northern parts of europe, russia (siberia), alaska and canada.