suppose a 65-kg person jumps from a height of 3.0 m down to the ground. A) What

Question

suppose a 65-kg person jumps from a height of 3.0 m down to the ground. A) What is the speed of the person just before landing? B) Estimate the average force on the person's feet exerted by the ground to bring the person to rest, if the knees are bent so the person's CG moves a distance d=50 cm during the deceleration period. C) Estimate the decelerating force if the person lands stiff-legged so d is about 1.0 cm. D) Estimate the stress in the tibia (area= 3.0 x 10^-4 m^2) and determine whether or not the bone will break if the landing is made with bent legs (d=50 cm). E) Estimate the stress and determine if the tibia will break in a stiff-legged landing (d= 1.0 cm)

Explanation / Answer

a) h = 3m; initial velocity u =0; a = 9.81 m/s2

v2 = u2 + 2 a s

v = (2 * 9.81 * 3)1/2 = 7.67 m/s (Ans)

b) displcement of COM s = 0.5m

u = 7.67 m/s; v = 0;

v2 = u2 + 2 a s

a = - u2/2s = - 58.83 m/s2

Force F = ma = 65*58.83 = 3824 N

c) displcement of COM s = 0.01m

u = 7.67 m/s; v = 0;

v2 = u2 + 2 a s

a = - u2/2s = - 2941.4 m/s2

Force F = ma = 65*2941.4 = 191194 N

d) Stress = F/A = 3824 / 3.0 x 10-4 =  1.27 * 107 Pa

e) Stress F/A = 191194 / 3.0 x 10-4 = 6.37 * 108 Pa

Breaking stress of Tibia is not provided

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