
05949236
j
2011e.00781
Kantrowitz, Robert
Neumann, Michael N.
Let\rq s do launch: More musings on projectile motion.
Pi Mu Epsilon J. 13, No. 4, 219228 (2011).
2011
Worcester Polytechnic Institute (WPI), Mathematical Sciences, Worcester, MA
EN
M50
I40
mathematical applications
physics
mechanics
trajectories
maximal displacement
optimal range
parametric equations
computer algebra
critical point equation
global maximum
local maximum
completion of a square
implicit differentiation method
Summary: This note addresses the motion of a projectile that is launched from the top of a tower and lands on a certain mountain. The main problem is to find a manageable formula for the initial angle of elevation that maximizes the distance the projectile travels. We first explore the extent to which computer algebra systems are helpful when applied to the classical critical point approach in this context. We then show how the shortcomings of this approach can be overcome by different methods that lead to a surprisingly simple formula for the best launch angle. As an illustration, optimal home runs for the game of tee ball are discussed.