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# Josh and Taylor, standing face-to-face on frictionless ice, push off each other, causing each to slide backward. Josh is much bigger than Taylor. After the push, which of the two is moving faster?

Solution

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$\text{\underline{\textbf{Given values:}}}$

$m_1>m_2$

\begin{align*} \tag{m_1 mass of Josh.}\\ \tag{m_2 mass of Taylor.}\\ \end{align*}

Bodies of greater mass are more inert, are more difficult to move.

The force with which Josh and Taylor act on the surface is their weight:

\begin{align*} W_1=\frac{m_1}{g} \tag{Equation 1.}\\ W_2=\frac{m_2}{g} \tag{Equation 2.}\\ \end{align*}

From Equations $1$ and $2$, we see that $W_1$ is greater than $W_2$, so to move Taylor, we need less force. Thus, Taylor will have greater acceleration $\implies$ greater speed.

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