Related Rates SOL APC.8c Luke Robbins, Sara Lasker, Michelle Bousquet

Steps to Solve any Related Rates Problem 1)Draw and label a diagram to visually represent the problem. 2)Define the variables. 3)List the givens and the unknown(s). 4)Brainstorm possible geometric or algebraic relationships between the variables and choose the relationship that contains all the givens and the unknown(s). 5)Differentiate the equation implicitly with respect to time. 6)Solve for the unknown variable(s). 7)Interpret the solution in the context of the problem.

The Problem

This diagram represents the ladder leaning against a wall. The wall has a 90 degree angle with the ground. Step 1) Draw and label a diagram to visually represent the problem. 10 feet/second 20 feet 5 feet

Step 2) Define the variables. x y z = 20 feet

Step 3) List the givens and the unknown(s). x = ? y = 5 feet z = 20 feet

x = ? y = 5 feet z = 20 feet Step 4) Brainstorm possible geometric or algebraic relationships between the variables and choose the relationship that contains all the givens and the unknown.

x = ? y = 5 feet z = 20 feet Step 4) Brainstorm possible geometric or algebraic relationships between the variables and choose the relationship that contains all the givens and the unknown. We choose this relationship because it and its derivative include all givens and the unknown.

5) Differentiate the equation implicitly with respect to time. x = ? y = 5 feet z = 20 feet Geometric Relationship

5) Differentiate the equation implicitly with respect to time. x = ? y = 5 feet z = 20 feet We know that z is constant, so we can plug in the value of z.

5) Differentiate the equation implicitly with respect to time. x = ? y = 5 feet z = 20 feet We derive the equation with respect to time, t.

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet At this point, we have two unknowns. Luckily we can calculate x with the original equation.

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet We will isolate x in the original equation as an intermediate solution.

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet We substitute in y to find what x is when y=5 feet.

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet

6) Solve for the unknown variable. x = ? y = 5 feet z = 20 feet

7) Interpret the solution in the context of the problem. x = ? y = 5 feet z = 20 feet