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A 42-inch vertical jump consists of two parts:

1. The first stage is the quick acceleration of the center of mass from a crouching to a standing position. The center of mass rises by 20 cm in this stage.

2. In the second stage, the player's feet leave the floor, and the center of mass rises 42 inches under the influence of gravity alone.

Answer :

The question is about average force. b. To find the average force on the feet, use the principle of work and energy. c. To find the average force on the feet when bending the legs, use the same principle. d. Compare the results of part (b) and (c) to draw conclusions about which way is better.

b. To find the average force on the feet, we can use the principle of work and energy. The work done on an object is equal to the change in its kinetic energy. The kinetic energy of the person's center of mass drops by only 1 cm vertically and 1 cm horizontally during the impact. Since the person's leg is stiff and straight, the movement is purely vertical and we can ignore the horizontal component. The change in kinetic energy is equal to the work done by the average force on the feet. The work done is equal to the force multiplied by the distance moved, which is 1 cm. Thus, the average force on the feet is the change in kinetic energy divided by the distance moved. Using the formula for kinetic energy, KE = 1/2mv^2, and plugging in the given values, we can calculate the average force on the feet.

c. To find the average force on the feet when the person bends his legs, we can use the same principle of work and energy. The person's center of mass drops by 50 cm vertically and 5 cm horizontally during the impact. Since the person bends his legs, both the vertical and horizontal components need to be considered. The change in kinetic energy is again equal to the work done by the average force on the feet. The work done is equal to the force multiplied by the distance moved, which is 50 cm vertically and 5 cm horizontally. We can calculate the average force on the feet using the given values and the formula for kinetic energy.

d. To compare the results of part (b) and (c), we can simply compare the average forces on the feet. We can draw conclusions about which way is better based on the magnitudes of the forces. If the average force on the feet is smaller, it means that less work is done on the body during the impact, which may be advantageous. Comparing the forces calculated in part (b) and (c), we can determine which way is better in terms of reducing the force exerted on the feet.

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