Streetlight Calculus Problem

Let $y = \sin{(x)}$

Find $\frac{dy}{dt}$ when $x = \frac{\pi}{4}$ given $\frac{dx}{dt} = 2 \frac{cm}{sec}$

A 10 by 6 foot rectangular swimming pool is being filled. Find the rate at which the height of the water rises if the hose is pouring at $20 \frac{{ft}^3}{hour}$

A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out?

During a night run, an observer is standing 80 feet away from a long, straight fence when she notices a runner running along it, getting closer to her. She points her flashlight at him and keeps it on him as he runs. When the distance between her and the runner is 100 feet, he is running at 9 feet per second. At this moment, at what rate is she turning the flashlight to keep him illuminated? Include units in your answer.