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In the standing broad jump, one squats and then pushes off with the legs to see how far one can jump. Suppose the extension of the legs from the crouch position is 0.600 m, and the acceleration achieved from this position is 1.25 times the acceleration due to gravity, g.

How far can they jump? State your assumptions. (Increased range can be achieved by swinging the arms in the direction of the jump.)

The distance of the jump is approximately:
a) 2.4 m
b) 3.0 m
c) 3.6 m
d) 4.2 m

User Kagronick
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1 Answer

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Final answer:

To calculate the standing broad jump distance, the jumper's final velocity after leg extension was determined using kinematic equations, then applied to projectile motion to estimate the horizontal distance. The calculated distance came out to be approximately 2 meters.

Step-by-step explanation:

Calculating the Distance of a Standing Broad Jump

To calculate how far a person can jump in a standing broad jump, we use principles of projectile motion. Assuming that the person converts all the acceleration from the leg extension into horizontal velocity, and the take-off and landing occurs at the same vertical level, we can find the horizontal distance covered during the jump.

Given that the acceleration is 1.25 times the acceleration due to gravity (g = 9.8 m/s2), the total acceleration (a) used in the jump is:

a = 1.25 * g = 1.25 * 9.8 m/s2 = 12.25 m/s2

Using the kinematic equation v2 = u2 + 2as and knowing initial velocity (u) is 0 (since the jump starts from rest), the final velocity (v) at leg extension is:

v = √(2 * a * s) = √(2 * 12.25 m/s2 * 0.600 m) ≈ 4.43 m/s

Now, we can apply projectile motion formula horizontally since we have horizontal velocity and the motion is unimpaired vertically assuming no air resistance:

Horizontal distance (d) covered in the air during the jump is:

d = v2 / g = (4.43 m/s)2 / 9.8 m/s2 ≈ 2 m

Therefore, the approximate distance covered in the standing broad jump would be 2 m, which is not listed explicitly among the options provided. In this scenario, a closely matched choice might be the best selection, but the answer likely lies between the options 2.4 m and 3.0 m.