A 6.5 m ladder leans against the wall of a cottage in Ontario…

Step 1. The height. $y = \sqrt{6.5^2 - 2.5^2} = \sqrt{42.25 - 6.25} = \sqrt{36} = 6\ \text{m}$.

Step 2. Differentiate. $x^2 + y^2 = 42.25$ gives $2x\,\dfrac{dx}{dt} + 2y\,\dfrac{dy}{dt} = 0$, so $\dfrac{dy}{dt} = -\dfrac{x}{y}\,\dfrac{dx}{dt}$.

Step 3. Put in the numbers. $\dfrac{dy}{dt} = -\dfrac{2.5}{6} \times 0.8 = -0.333\ \text{m/s}$.