This problem is taken from Ahlborn\'s Zoological Physics, P 5.2. Two young peopl

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. B 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?

Explanation / Answer

b) before proceeding, we have to find impact speed, u

u2= 2*g*h=2*9.8*2=39.2

u=root of 39.2 =6.26m/s

Now, for finding decelration, u=6.26m/s, v=0, s=5cm=0.05m

v2=u2-2as

0=39.2 - 2*0.05*a

a=39.2/0.1= 392 m/s2

Force on his sole=70* 392 m/s2 = 27440 N

c) for girl, h=2-0.5=1.5m

u2=2gh =2*9.8*1.5=29.4...where u is impact velocity

Now, for finding decelration, u2=29.4, v=0, s=0.5m

v2=u2-2as

0=29.4 - 2*0.5*a

a=29.4/1= 29.4 m/s2

Force= 29.4*65= 1911 N

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