# Related Rates Calculus Tutorial

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.

## Related Problems

Let $y = 2(x^2 - 3x)$

a. Find $\frac{dy}{dt}$ when $x = 3$ given $\frac{dx}{dt} = 2$

b. Find $\frac{dx}{dt}$ when $x = 1$ given $\frac{dy}{dt} = 5$

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 man 6 ft tall is walking away from a streetlight 20ft high at a rate of 5ft/sec. At what rate is the tip of his shadow moving when he is 24 feet from the lightpost and at what rate is the length of his shadow increasing?