A head-butter can accelerate himself from rest to head-butting speed of 8.5 m/s.

Question

A head-butter can accelerate himself from rest to head-butting speed of 8.5 m/s. Since the upper body is involved in a properly executed head-butt, the effective mass of the head is 24kg. Assume the direction of the head moves at positive x direction and assume linear motion.

a) At the moment of impact, what impulse does the head butter produce?

b) If the head butter reaches the butting speed of 8.5 m/s in 0.5 seconds, what power must his muscles produce?

c) If he head-butts an opponent in the face and his head comes to rest in a time of 0.15 seconds, what is the magnitude and direction of the force that the opponent

Explanation / Answer

a) impulse =m(v-u) =24*8.5 =204kg.m/s...................

b) power =work/time =0.5*m*v^2/0.5= 1734 W.........

c) F =m*(v-u)/t=24*(-8.5)/0.15=-1360N i.e along -ve x-axis

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