Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 08/Statement

Jenna is riding off a snowboarding ramp while her father takes a video of her flight. The ramp tilts up with a slope of 1/2. Her father stands 3 meters in front of the ramp with his camera pointed at the ramp and held at the same level as the top of the ramp. The angular elevation of the camera, $\theta (t)$, starts at 0 and increases with time so that the camera follows Jenna. When Jenna is a horizontal distance x from the ramp, she is a vertical distance $f(x)$ above the top end of the ramp. She is moving horizontally at a speed of 2 m/s as she leaves the ramp. How rapidly must Jenna’s father be rotating the camera so as to follow her flight path just as she leaves the ramp ($x=0$)? Note that $f(0)=0$ and $f'(0)=1/2$.