Please show ALL work! Thanks! A bullet of mass 12.0g is shot directly upwards at

Question

Please show ALL work! Thanks!

A bullet of mass 12.0g is shot directly upwards at 1.20 km/s, through a hole in a shelf, to hit a solid wood block directly below its center of mass. The block has a mass of 4.25 kg. The bullet re-emerges from the block on the far side, continuing to move directly upwards at 0.400 km/s. a) What is the maximum height that the block will rise above its initial position? b) What is the maximum amount of energy in the above collision that could go into heating of the block and bullet? c) If the collision is instead completely inelastic, what is the maximum height that the block will rise above its initial position?

Explanation / Answer

a) by momentum conservation, speed of block is given by v,

0.012*1200 = 0.012*400 + 4.25v

v = 0.012*800/4.25 = 2.259 m/s

maximum height = v^2/2g = 2.259^2/(2*9.8)

= 0.2604 m

b) energy in heating = initial KE - final KE

= 0.5*0.012*1200^2 - 0.5*0.012*400^2 - 0.5*4.25*2.259^2

= 7669 J

c) v =   0.012*1200/(4.25+0.012) = 3.3787 m/s

maximum height h = v^2/2g = 3.3787^2/(2*9.8)

= 0.582 m

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