A 5.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 3.

Question

A 5.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 3.3 kg object moving in the -x direction at 4.0 m/s. Find the final velocity of each mass for each of the following situations. (Take the positive direction to be +x.) (a) The bodies stick together. ? m/s (5.5 kg mass) ? m/s (3.3 kg mass) The collision is elastic. ? m/s (5.5 kg mass) ? m/s (3.3 kg mass) (c) The 5.5 kg body is at rest after the collision. ? m/s (5.5 kg mass) ? m/s (3.3 kg mass) (d) The 3.3 kg body is at rest after the collision. ? m/s (5.5 kg mass) ? m/s (3.3 kg mass) (e) The 5.5 kg body has a velocity of 4.0 m/s in the -x direction after the collision. ? m/s (5.5 kg mass) ? m/s (3.3 kg mass) Are the results in (c), (d), and (e) "reasonable"? Explain.

Explanation / Answer

conservation of momentum

m1u1 +m2u2 = m1v1+ m2v2

conservation of energy
m1u1^2 +m2u2^2 = m1v1^2+m2v2^2

from this equation, we get

v1 = -2.125 so it is in -x direction

v2 = 3.375 so it is in x direction

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