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

Answer:

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

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,

$F_1=-F_2$

$m_1a_1=-m_2a_2$

$a_1=-\dfrac{m_2a_2}{m_1}$

$a_1=-\dfrac{37\times 2.2}{62}$

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

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

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