Related Rates SOL APC.8c

Related RatesSOL APC.8cLuke Robbins, Sara Lasker, Michelle BousquetSteps to Solve any Related Rates ProblemDraw and label a diagram to visually represent the problem.Define the variables.List the givens and the unknown(s).Brainstorm possible geometric or algebraic relationships between the variables and choose the relationship that contains all the givens and the unknown(s).Differentiate the equation implicitly with respect to time.Solve for the unknown variable(s).Interpret the solution in the context of the problem.The ProblemThis 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/second20 feet5 feetStep 2) Define the variables.xyz = 20 feetStep 3) List the givens and the unknown(s).x = ?y = 5 feetz = 20 feetx = ?y = 5 feetz = 20 feetStep 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 feetz = 20 feetStep 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 feetz = 20 feetGeometric Relationship5) Differentiate the equation implicitly with respect to time.

x = ?y = 5 feetz = 20 feetWe 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 feetz = 20 feetWe derive the equation with respect to time, t.6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feetAt this point, we have two unknowns. Luckily we can calculate x with the original equation.6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feetWe will isolate x in the original equation as an intermediate solution.6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feetWe substitute in y to find what x is when y=5 feet.6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feet6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feet6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feet6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feet6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feet6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feet6) Solve for the unknown variable.x = ?y = 5 feetz = 20 feet7) Interpret the solution in the context of the problem.x = ?y = 5 feetz = 20 feet