Related Rates Worksheet - Intro
For this worksheet, we are going to explore some related rates problems. The first couple will have steps for you to follow, while the last few will have you complete the process on your own.
1. Two people on bikes are at the same place. One of the bikers starts riding directly north at a rate of 8 m/sec. The second stars to ride directly east at a rate of 5 m/sec. At what rate is the straight line distance between the two riders increasing when the first person is 160 meters from the starting point (so the second is 100 m from the start)?
(a) Draw a picture of the scenario. Be sure to put both the 8 m/sec and 5 m/sec on the picture.
(b) Your picture should be a triangle. Label the sides of this triangle (as variables).
(c) What is the rate of change that we are looking for? State this in words, as well as in "calculus" terms.
(d) Using the columns below, identify any rates of change we know, any constants and any instants we are given. Name them in the context of the variables you have chosen.
Rates
Constants
Instants