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Whenever I look at the jumping events in track-and-field, I do not see human bodies in motion; instead (perhaps due to my mathematics background) I see vectors in motion. A vector is an arrow that describes the direction and magnitude of a moving object. Athletes cannot jump higher or further without taking into account Newton's laws of physics. This article will explain how vectors are applied in the various track-and-field jumping events: long jump, triple jump, high jump, and pole vault. More specifically, I will illustrate the impact of horizontal velocity in determining maximum height and distance in the jumps. In all the examples velocity vectors were used; however, they do not consider the application of forces that produce the motion we observe.
One example of vectors can be given with a 100 m sprinter. If an athlete runs toward the finish line with an average velocity of 10 m/s, then he should cross the line in 10 seconds flat. The athlete's velocity vector is represented by Vector A (see Figure 1). If there were a headwind of 2 m/s, as represented by Vector B, then the athlete's motion would be impeded and overall speed would decrease. Vector C represents the resultant vector, whereby the athlete's velocity has decreased to 8 m/s.
Conversely, if there were a tailwind, the athlete would run faster if Vector B were reversed (see Figure 2).
Long Jump
In the long jump, the speed of the athlete before takeoff has the greatest impact on absolute distance (Hay, Miller, & Caterna, 1986). Let us consider the following example: a jumper attempts to long jump at a take-off angle of 20 with a take-off velocity of 8 m/s (see Figures 3 and 4). On her second attempt, she has the same take-off angle, but has a take-off velocity of 10 m/s. If all other factors are the same, she will jump further on her second attempt. The horizontal velocity of the jumper combines with the vertical velocity placed at the take-off board to form a resultant vector. In the vertical plane, the force of...