Related Rates Math Example 2

Solution

1. 1
   Let $x$ = distance of base from wall, $y$ = height of top. Pythagorean: $x^2 + y^2 = 169$.
2. 2
   When $x = 5$: $y = \sqrt{169 - 25} = 12$ ft.
3. 3
   Differentiate with respect to $t$: $2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$.
4. 4
   Substitute: $2(5)(5) + 2(12)\frac{dy}{dt} = 0 \Rightarrow 50 + 24\frac{dy}{dt} = 0$.
5. 5
   $\frac{dy}{dt} = -\frac{50}{24} = -\frac{25}{12}$ ft/s.