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 α. What is the optimal angle α 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 α. 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.

James S.
, 4th ed. (
), p.
International Ski Federation
, “
Standards for the Construction of Jumping Hills—2008
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