Teaching Mathematics and its Applications Advance Access originally published online on August 11, 2009
Teaching Mathematics and its Applications 2009 28(3):123-130; doi:10.1093/teamat/hrp015
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An application of calculus: optimum parabolic path problem
ehzade Mehmet Juniory High School, Manisa, Turkey
Department of Mechanical Engineering, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
Department of Mathematics, Georgetown University, Washington DC, USA
Email: mpak{at}bayar.edu.tr
Submitted March 2009; accepted July 2009
A practical and technological application of calculus problem is posed to motivate freshman students or juniory high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object for which the work done by variable coefficient air friction force is minimum is determined. If a flying object follows the determined path, energy requirement would be less compared with other parabolic or linear paths.
Merve Atasever is currently a student in ehzade Mehmet Juniory High School. She is expecting to graduate in Summer 2009 and continue her education in a University.
Mehmet Pakdemirli received his BS degree in Mechanical Engineering from Bogazici University, Istanbul in 1985 and MS degree from the same university in 1987. He completed his PhD studies in 1991 from Istanbul Technical University. He studied as a postdoctoral research associate in Virginia Tech for 2 years. He became assistant professor in 1993, promoted to associate professor in 1994 and finally to full professor in 2003 in Celal Bayar University, Manisa, Turkey. He visited the University of Michigan for 6 months in 1996 and King Fahd University of Petroleum and Minerals in Saudi Arabia in 2003–2004. He is currently professor and department head of Mechanical Engineering in Celal Bayar University. He has authored, co-authored some 100 papers in internationally refereed journals.
Hasan Ali Yurtsever received his BS degree in physics from Bogazici University, Istanbul in 1989. He completed his graduate degree in Mathematics and received his PhD in 1998. He joined the Mathematics Department of Fatih University, Istanbul, as an assistant professor of Mathematics in 1999 and has taught at Florida International University, Miami. He has been a research scholar at Georgetown University since 2004.