Calculus 1: Related Rates Problems

A 20 foot ladder is leaning against a wall and the base of the ladder is sliding away at 6 feet a second. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet from the wall?

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 $\frac{dy}{dt} = 5$

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?