Zadanie 9d, Paper 2, listopad 2024, TZ2, Matematyka AA IB SL

All trigonometric arguments are in radians. Let $f(x)=8\cos(2\pi x)$ and $g(x)=-15\sin(2\pi x)$. Their sum can be written $a\cos(b(x-c))$ with a,b,c>0. In a separate motion model, a conveyor carries a scanner along a straight track with velocity $v(t)=7+3\sin(\pi(t+2)/15)$ metres per second for t≥0 seconds. Identical inspection checkpoints occur whenever the scanner reaches its maximum velocity. The scanner keeps moving forward.