Final answer:
In jumping, one stores elastic potential energy in a deep crouch that gets converted to kinetic energy for a higher jump. Bending the knees when landing is crucial for decreasing the impact force.
Step-by-step explanation:
The question relates to the transformation of energy during jumping and the optimal strategy for achieving the maximum height or distance in a jump. When you move downward quickly into a deep crouch before jumping, you are stretching your tendons and muscles, storing elastic potential energy. This stored energy is then converted into kinetic energy as you push off the ground, allowing you to jump higher or farther than if you pushed off from a stationary crouch.
Bending your knees when leaping off of a high place like a bench is crucial because it increases the time of impact when you land. According to the impulse-momentum theorem, increasing the time of impact decreases the force exerted on your body, which can prevent injury. This concept is also why rolling after a fall or using a parachute is beneficial as it extends the time over which the force acts, thereby spreading out the force and reducing the risk of damage.
Regarding the standing broad jump, the distance one can jump is influenced by the extension of the legs and the acceleration achieved, as well as by swinging the arms in the direction of the jump. Force calculations involving jumping from a height to the ground often include the effects of impact forces on the joints, and how bending the knees can alter the magnitude of these forces by increasing the stopping distance.