Question

A 62 kg boy and a 37 kg girl use an elastic rope while engaged in a tug-of-war on a friction-less icy surface. If the acceleration of the girl toward the boy is 2.2 m/s², determine the magnitude of the acceleration of the boy toward the girl.

Answer in units of m/s².

Answer 1

The magnitude of the acceleration of the boy toward the girl is
`1.31\ m/s^2`

Step-by-step explanation:

It is given that,

Mass of the boy,
`m_1=62\ kg`

Mass of the girl,
`m_2=37\ kg`

The acceleration of the girl toward the boy is,
`a_2=2.2\ m/s^2`

To find,

The acceleration of the boy toward the girl.

Solution,

Let
`a_1` is the magnitude of the acceleration of the boy toward the girl. We know that force acting on one object to other are equal in magnitude but opposite in direction. So,

`F_1=-F_2`

`m_1a_1=-m_2a_2`

`a_1=-(m_2a_2)/(m_1)`

`a_1=-(37* 2.2)/(62)`

`a_1=-1.31\ m/s^2`

`|a_1|=1.31\ m/s^2`

So, the magnitude of the acceleration of the boy toward the girl is
`1.31\ m/s^2`