For part 1, click the link below
The best long jumpers center of mass travels between 18 and 21 degrees from horizontal(Beres et al., 2014). To takeoff at this angle, long jumpers must apply vertical forces at the take off board to achieve lift. In regards to projectile motion, one might assume that 45 degrees would be the optimal takeoff
angle; however the human body is not an inelastic object, and therefore must takeoff at an angle that favors the human body’s ability to apply force. Because the athlete is required to create lift during very high velocities, the athlete implements a lowering step, or penultimate step prior to takeoff. During this step, the athlete preserves horizontal velocity and lowers their center of mass(Lees et al., 1994; Linthorne, 2008; Makaruk, Porter, Starzak, & Szymczak, 2016). Traditionally, athletes perform the penultimate step by placing the foot in front of the body so that the font shin is perpendicular to the ground at touchdown, and then roll over the step, leaving their foot behind the body(Dyson, Woods, & Travers, 1986). The athlete is actively projecting their body forward, but should not attempt to lower too much. If the athlete lowers too much, they will likely be unable to apply sufficient eccentric forces and lose optimal positions required to preserve takeoff velocity and apply large horizontal and vertical forces(Hay, 1993). Additionally, if the center of mass is lowered too much, the athlete will have an increase in negative vertical velocity, and have to apply additional vertical forces to achieve the appropriate amount of lift(Hay, Miller, & Canterna, 1986; Linthorne, Guzman, & Bridgett, 2005). If this occurs, the athlete will likely break, similar to high jump, and decrease the ever-important horizontal takeoff velocity resulting in a shorter jump distance.
During the takeoff, the athlete places their foot in font of the center of mass. The further in front of the center of mass the foot is placed, the larger the vertical and breaking forces (Dyson et al., 1986). There are two primary reasons for this: the first is that the athlete has more time to apply vertical force, and the second is that the athlete must break as a result of the force vectors occurring on the ground (Lees et al., 1994). At takeoff, the athlete’s leg functions as a stiff lever that the center of mass vaults over top of(Beres et al., 2014; Graham-Smith & Lees, 2005; Lees et al., 1994). Simultaneously, the athlete accelerates the opposing knee forward to increase vertical impulse through a blocking mechanism, and raise the athlete’s center of mass prior to takeoff(Dyson et al., 1986). After takeoff, the athlete’s center of mass has a set trajectory.
Based on the laws of motion, this trajectory cannot be changed unless external forces were to be placed upon the athlete. However, because of the high flight times, and the way in which the mass is distributed, the body will naturally begin to display forward rotation(Dyson et al., 1986). To slow this rotation, the athlete may utilize the hitch kick, or enlongate their body mid-flight (Dyson et al., 1986). To initiate the landing phase, the athlete pulls their legs towards their buttocks and “shoots” their legs and feet as far forward as possible. To move the center of mass forward, the athlete may also display a forward lean. Upon making contact with the sand, the coach is able to assess how successful the athlete was in executing the landing phase by watching how high the hips relative to the top plane of the sand. The athlete then pulls their hips forward, so as to minimize how far their hips are from the front edge of the takeoff board.
In summary, long jump is heavily dependent on the horizontal and vertical forces applied throughout the run up, penultimate step, and takeoff. The best jumpers are very fast and put their bodies in the correct positions at the correct times, optimizing the transfer of speed from the run up to the takeoff.
For the reference list, see part 1.