A 57 kg boy and a 45 kg girl use an elastic rope while engaged in a tug-of-war on a frictionless icy surface.

Question

If the acceleration of the girl toward the boy is 1.5 m/s2, determine the magnitude of the acceleration of the boy toward the girl.
Answer in units of m/s2

Answer 1

Since the same force is acting on both,
the acceleration of the boy will be less
by their mass ratio:

a=(45kg/57kg) * 1.5m/s^2 = 1.184 m/s^2.

Alternate Method.
Fg = ma = 45 * 1.5 = 67.5 N. = Force
acting on girl.

Fb = Fg = 67.5 N.
a = Fb/m = 67.5 / 57 = 1.184 m/s^2. =
Acceleration of boy.