Minimal Path Project Kyla Semones Cousino High School

Minimal Path Project Kyla Semones Cousino High School

Problem A student, who shall not be named, is always running late for school in the morning. This student rides their bike to school. When rushing they are able to ride their bike at about 6 ft/s. The usual route they take is shown in the diagram; 750 ft down Martin Rd. making a left onto Cosgrove Dr. traveling 1000 ft until they reach MMSTC. This student wants to work on getting to school on time. Instead of waking up earlier the student decides to cut across the field to get to school faster. If the student can only travel 4 ft/s across the field find the point on Cosgrove Dr. that the student should ride to minimize the total time. 2

Diagram 3

Solution § 4

Solution § 5

Solution § 6

Solution § 7

Solution § 8

Answer the Question This student should ride their bike to a point about 671 ft from the corner of Cosgrove Dr. and Martin Rd. to minimize the total time. 9

st 1 Derivative § 10

st 1 Derivative The slope changes from negative to positive. The graph goes from decreasing to increasing therefore minimum must occur between 670 ft and 671 ft. This minimum occurs at 670. 8204 ft 11

Recap It has been proven with calculus that the student should ride their bike to a point about 671 ft from the corner of Cosgrove Dr. and Martin Rd to minimize the total time. 12

Works Cited Provo Bike-to-School Week. Digital image. Bike Provo. 8 Sept. 2014. Web. 13

14

15