As a projectile of mass $m$ kilograms travels through air, it experiences a frictional force - HSC - SSCE Mathematics Extension 2 - Question 8 - 2022 - Paper 1

In this problem, we need to consider the forces acting on the projectile. The gravitational force acts downward and is represented by $-mg$. The frictional force, which opposes the motion, is proportional to the square of the velocity and points in the opposite direction, thus given by $-kv$.

The overall equation representing this system based on Newton's second law, $F = ma$, can be expressed as:

$$egin{pmatrix} -mg \ -kv rac{dx}{dt} \ rac{dy}{dt} \ ext{(where v = rac{dy}{dt})}\ \ ext{As the net force equals mass times acceleration, the correct equation is:}\ ext{Therefore, the answer is option B: } egin{pmatrix} -mg \ -kv egin{pmatrix} rac{dx}{dt} \ rac{dy}{dt} \ \ \ \ \ \