Optimal Ski Jump

Krzysztof Rębilas

Abstract

Consider a skier who goes down a takeoff ramp, attains a speed "V", and jumps, attempting to land as far as possible down the hill below (Fig. 1). At the moment of takeoff the angle between the skier's velocity and the horizontal is [alpha]. What is the optimal angle [alpha] that makes the jump the longest possible for the fixed magnitude of the velocity "V"? Of course, in practice, this is a very sophisticated problem; the skier's range depends on a variety of complex factors in addition to "V" and [alpha]. However, if we ignore these and assume the jumper is in free fall between the takeoff ramp and the landing point below, the problem becomes an exercise in kinematics that is suitable for introductory-level students. The solution is presented here.
Author Krzysztof Rębilas (FoAaE / DoChaP)
Krzysztof Rębilas,,
- Department of Chemistry and Physics
Journal seriesPhysics Teacher (The), ISSN 0031-921X, e-ISSN 1943-4928, (A 15 pkt)
Issue year2013
Vol51
Pages108-109
Publication size in sheets0.3
DOIDOI:10.1119/1.4775534
URL http://scitation.aip.org/content/aapt/journal/tpt/51/2/10.1119/1.4775534
Internal identifierWRE/2013/294
Languageen angielski , en angielski
Score (nominal)15
Publication indicators WoS Citations = 1
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