Optimal Ski Jump

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 p...

Full description

Saved in:
Bibliographic Details
Published in:The Physics teacher 2013-02, Vol.51 (2), p.108-109
Main Author: Rebilas, Krzysztof
Format: Article
Language:English
Subjects:
College Science
Introductory Courses
Motion
Problem Solving
Science Instruction
Scientific Principles
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0031-921X
1943-4928
DOI:10.1119/1.4775534