Why? The Science of Athletics

SOME MATHEMATICS IN ATHLETICS On working this out it will be found that the impulse of the force required is : (a) for 24ft. per sec., 350 units of impulse. (b) " 20ft. " 9!0 " " (c) , 17·14 ft. , 1320 , , This shows clearly that the greater the speed acquired in the approach run, the less units of impulse will be needed for the jump. In other words, the greater the speed a man can command in the run-up, the more units ?f impulse he will have at his disposal to put into the Jump. Now let us look at the question from the point of view of .the jump i~self, and, to eliminate all complications of speed-velocity and increased acceleration, we will take the case of a man weighing, let us say, 168lbs., who intends to jump a distance of 10 ft. from a stationary position. He will, of course, swing his arms, lean forward, and crouch to generate the impulse for his spring, but at the actual instant of take-off his body will be fully extended before his toes leave the board. The velocity with which he leaves the board will be one of 17·8 ft. per second, and his initial horizontal and vertical velocities will be 12·6 ft. per sec., the compressed force exerted being 93·45 lb., and the kinetic energy 831·6 foot-lb.* If he jumps at th.e correct angle of 45 degrees, according to all laws of dynamics the highest point in his parabola of flight will be reached at 2 ft. 6 ins. midway between take-off and landing. Turn back now to Fig. 93· During the first part of the jump from A to H the jumper will be fighting to combat the resistance due to the attraction of gravity, but after he has passed H (the high point in his parabola of flight) gravity will assist him to increase the length of his * Force is that which changes, or tends to change, the state of rest, or uniform ~otion, of a body. Kinetic energy is the energy due to the motion of a body, and is mcreased by the amount of work the body can perform against the impressed forces before its velocity is destroyed.