A slug of mass 0.100 kg moving straight upward at 50.0 m/s collides with a 0.400 kg wooden block that is 20.0 cm long on a side. The slug embeds in the soft wood and as a result the block+bullet fly some distance up into the air before falling back to the ground.
In this problem we will compare two scenarios a "direct center" hit of the slug in the block, that results in zero spinning, and an "off center" hit that results in both upward translational and rotational motion.
(a) For the direct hit, what is the velocity of slug+block immediately after the hit, and how high will it go?
(b) What is the loss of kinetic energy immediately before/after the hit?
(c) For the off-center hit, assume the slug hits and embeds at a point 8.00 cm to one side of the block's center of mass. What is the velocity of slug+block after the hit, and how high does it go?
(d) What is the rotation rate after the hit, and about which point does the slug+block rotate?
(e) What is the loss of kinetic energy immediately before/after the hit in the off-center hit case?
(f) In which scenario would the slug embed more deeply, the Direct Hit or Off Center Hit? Or will they be the same? Explain your reasoning.
(g) The direct hit block should go straight up, and fall straight down. How about the off-center hit block does it fly straight up & back down as well, or is there a deflection to one side? If so, to which side? Explain your reasoning.