The time of flight, range and the angle which maximizes the range of a projectile in a linear resisting medium are expressed in analytic form in terms of the recently defined Lambert W function. From the closed-form solutions a number of results characteristic to the motion of the projectile in a linear resisting medium are analytically confirmed, and asymptotic and approximate expressions valid within the weak and strong damping limits are developed. The problem provides an accessible account of the increasingly applicable Lambert W function and highlights much of the important mathematics associated with this simple yet rapidly emerging 'implicitly' elementary function.
|Number of pages||21|
|Journal||International Journal of Mathematical Education in Science and Technology|
|Publication status||Published - Jun 15 2006|
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Applied Mathematics