Calculus Related Rates Word 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 street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole?

A boat is pulled in by means of a winch on a dock 12 ft above the deck of the boat. If the winch pulls in rope at the rate of 4 ft/sec, determine the speed of the boat when 13 feet of rope is out.