## 4 Discussion
pointed out that high jumpers can generate very powerful takeoff energy in a very short time of 0.1\(\sim\)0.2 s; the moment from when the jumper's takeoff foot touches the ground to the moment when the takeoff foot leaves the ground is only 0.1\(\sim\)0.2 s [58], and many studies have also confirmed that having a better RFD could produce faster movements and greater explosive strength [61; 62; 63]. The momentary GRF values of participants No. 9, 10, and 11 in this study were the highest among all participants, but their RFD values were the lowest among all participants. This phenomenon shows that a strong GRF does not necessarily correspond with a good RFD [64] because the RFD is related to the contact time of the soles of the feet, and the GRF is related to body weight and muscle mass. Therefore, the variability in both was large, as evidenced in many studies [65; 66; 67]. In addition, the relationship between the RFD and the explosive strength of participants No. 9, 10, and 11 is confusing. The basis of explosive strength is muscle strength, and explosive strength determines the RFD performance [68]. RFD is derived from the force or the slope of the force-time curve of voluntary muscle contraction [69,70]; thus, the calculation formula of the RFD is as follows: RFD = force (moment) \(\div\) force time (time). Explosive strength refers to the ability to generate the maximum power in the shortest time, which is a result of the combination of speed and power [15]; thus, the formula for calculating explosive strength is as follows: explosive strength (P) = power (F) \(\times\) velocity (V). RFD is associated with instantaneous time, and explosive strength is associated with speed; therefore, there was a discrepancy between the two, a view held by many scholars [71]. According to research, it takes approximately half a second (0.5 s = 500 milliseconds) for muscle contraction to reach maximum strength, and the ground contact time when running is within one-fifth of a second (0.20 s = 200 milliseconds) [63]; the faster the speed, the shorter the ground contact time, but the greater the strength required. Therefore, improving strength and shortening the RFD time is more important than developing maximum strength [72]. Thus, although maximizing strength has its benefits, developing maximal strength is not imperative for every sport. If technical aspects are not considered, those who can exert greater strength in a shorter period of time will have an opportunity to gain the upper hand [73]. Therefore, RFD relies on muscle contraction and is a key indicator of explosive strength. The results of the CMJ experiment found that the duration of passage of participant No. 3 reached 0.643 s, and the jump height reached 0.624 m, which was the best performance among all participants, which showed that the PT program had some positive effects on improving explosive strength. These data corroborate that the reaction force generated in the CMJ remains for the 0.643 s duration of passage. After PT, it was found that the explosive strength of the lower limbs increased in the duration of passage, and the jump height increased [74,75]. Research by [PERSON] et al. demonstrated that high explosive strength is composed of three factors: the size of the muscle cross-section, the stiffness of the muscle mass, and neural adaptation [76]. In this study, PT recruited the required motor units and stimulated the activation of motor nerves during training so as to quickly reach the maximum force; thus, the RFD, the duration of passage, and the jump height were enhanced. In addition, from the force plate operation, it was found that the muscle contraction of the participants before takeoff enabled the muscles to generate the energy required for movement. This energy was temporarily stored in the muscle cells. When the muscles contract rapidly to produce muscle stretching, the maximal force produced at this time improves the muscle explosive strength [5,77,78]. There were several limitations in this study.