## Related questions with answers

Calculate the magnitude of the linear momentum for the following cases: a 15.0-g bullet moving with a speed of 300 m/s.

Solutions

VerifiedIn this problem, we are given the mass and speed of several objects, and we calculate the magnitude of the linear momentum. For this part, the object is a proton with mass $m = 15.0 \times 10^{-3}~\mathrm{kg}$ and speed $v = 300~\mathrm{m/s}$.

$\textbf{(b)}$ Here given that the mass of the bullet is $m_{\text{b}} = 15\,\mathrm{g} = 0.015\,\mathrm{kg}$.

Speed of the bullet is $v_{\text{p}} = 300\,\mathrm{m\,s^{-1}}$.

As we know the linear momentum of a particle having mass $m$ and velocity $\vec{v}$ is given by

$\begin{align*}\\ \vec{p} = m\,\vec{v}\tag{1} \end{align*}$

The magnitude of the momentum is given by

$\begin{align*}\\ p = m\,v\tag{2} \end{align*}$

Hence from the above equation (2), the magnitude of the linear momentum of the bullet is given by

$\begin{align*}\\ p_{\text{b}} & = m_{\text{b}}\,v_{\text{b}}\\ & = 0.015\,\mathrm{kg}\,\times 300\,\mathrm{m\,s^{-1}}\\ & = 4.5\,\mathrm{kg\,m\,s^{-1}} \end{align*}$

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