Q8

As a projectile of mass $m$ kilograms travels through air, it experiences a frictional force. The magnitude of this force is proportional to the square of the speed $v$ of the projectile. The constant of proportionality is the positive number $k$. The position of the particle at time $t$ is denoted by $\begin{pmatrix}x\\y\end{pmatrix}$. The acceleration due to gravity is $g\,\mathrm{m\,s^{-2}}$.

Based on Newton’s laws of motion, which equation models the motion of this projectile?

A. $\begin{pmatrix}0\\-mg\end{pmatrix}+kv\begin{pmatrix}\dot x\\\dot y\end{pmatrix}=m\begin{pmatrix}\ddot x\\\ddot y\end{pmatrix}$

B. $\begin{pmatrix}0\\-mg\end{pmatrix}-kv\begin{pmatrix}\dot x\\\dot y\end{pmatrix}=m\begin{pmatrix}\ddot x\\\ddot y\end{pmatrix}$

C. $\begin{pmatrix}0\\-mg\end{pmatrix}+kv^2\begin{pmatrix}\dot x\\\dot y\end{pmatrix}=m\begin{pmatrix}\ddot x\\\ddot y\end{pmatrix}$

D. $\begin{pmatrix}0\\-mg\end{pmatrix}-kv^2\begin{pmatrix}\dot x\\\dot y\end{pmatrix}=m\begin{pmatrix}\ddot x\\\ddot y\end{pmatrix}$