A 58 kg boy and a 38 kg girl use an elastic rope

Question

while engaged in a tug-of-war on a frictionless
icy surface.
If the acceleration of the girl toward the
boy is 3.1 m/s
2
, determine the magnitude of
the acceleration of the boy toward the girl.
Answer in units of m/s
2

Answer 1

The forces will be equal( but opposite).
Force equals mass times acceleration.

Let m = 38kg (the girl's mass)
Let a = 3.1m/s^2 (the girl's acceleration)
Let n = 58kg (the boy's mass)
Find b (the boy's acceleration).
Such that: m*a = -n*b