This activity sheet illustrates four common related rate questions that appear in all calculus AB and BC courses.
• The first problem presents two cars that are traveling away from each other on roads that are perpendicular to each other. The problem can be modeled with a right triangle so the Pythagorean Theorem becomes the function to associate with this problem. This equation can be used to generate a related rates equation. From the information that is given students can determine the rate at which the distance between the two cards is increasing.
• The second problem presents a ladder leaning against a wall. The ladder is sliding down the wall so the foot of the ladder is moving away from the wall. Again the problem can be modeled with a right triangle so the Pythagorean Theorem is appropriate to use to determine how the rates are related. Students will need to reason that the length of the ladder is constant so the related rate of the length of the ladder is zero.
• The third problem presents a conical shape reservoir being filled with water. Since the volume of the water will be considered the formula for the volume of a cone will be used to generate the related rates in this problem. Students must find the rate of change of the height of the water when the water is two-thirds full.
• The fourth problem presents a person walking away from a lamppost. The students will use two overlapping similar right triangles to find the rate at which the length of the person’s shadow is increasing and the speed of the top of person’s shadow. The two similar triangles will allow the students to write a proportion that can be used to generate a related rates equation.
There are four additional related rates scenarios included for after the four questions are completed on the activity sheet.
A full set of solutions is included for the four exercises on the activity sheet and the four additional exercises.
Comments from buyers:
• Great resource!
• Worked well as part of an intro to related rates. Day 1: I presented the problems in lecture format and had students "redo" them using the worksheets as homework/practice. Day 2: Students asked clarifying questions and completed the "practice problems" in pairs. Thank you!
• Great Resource ! Thanks !
• Great! thanks for sharing!
• Does an excellent job breaking down the concepts of Related rates. Definitely recommend as a precursor to any formal notes on the subject.
Please check out the Activity Sheet on Related Rates that is also in my store.