Question

This problem is taken from Ahlborn's Zoological Physics, P 5.2. Two young people jump down from a height of h = 2.0 m onto the forest floor which has a mud hole and a rocky flat. The boy (M = 70 kg) lands with stiff legs on the muddy ground, which "gives" so that he depresses the ground by Delta_y = 5 cm when being decelerated from the impact velocity U_0 to 0. Determine the impact speed U_0. Calculate the deceleration (negative acceleration of the center of mass of the boy during landing), and determine the force on the soles of his shoes during impact. The girl (M = 65 kg) lands on the rock, but in order to reduce the impact force she lands with soft knees and moves her center of gravity relative to her feet by Delta y = 0.5 m as she lands. What is the impact force on her soles of the feet during the landing?

Answer 1

(a) Using conservation of energy

(Potential energy at height) + (kinetic energy at height) = (Potential energy at ground) + (kinetic energy at ground)

(mgh) + (1/2m*0²) = (mg*0) + (1/2 mU_o²)

U_o = (2gh)^1/2

U_o = (2 * 9.8 * 2)^1/2

U_o = 6.26 m/s

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(b) Using relation v² - U_o² = 2aΔy

0 - (6.26)² = 2 a (0.05)

a = - 391.88 m/s²

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