Final answer:
In an elastic collision, both momentum and kinetic energy are conserved. The velocity of the 3.00-kg object after the collision is 20.0 m/s west.
Step-by-step explanation:
In an elastic collision, both momentum and kinetic energy are conserved.
Let's consider the collision between the 3.00-kg object and the 5.00-kg object. The total momentum before the collision is given by:
Initial momentum = m1v1 + m2v2
where m1 and v1 are the mass and velocity of the first object, and m2 and v2 are the mass and velocity of the second object. Substituting the given values:
Initial momentum = (3.00 kg)(-20.0 m/s) + (5.00 kg)(-12.0 m/s) = -60.0 kg·m/s + (-60.0 kg·m/s) = -120.0 kg·m/s
Since the collision is perfectly elastic, the total momentum after the collision is also -120.0 kg·m/s. Let the final velocity of the 3.00-kg object be vf. The total momentum after the collision can be written as:
Final momentum = m1vf + m2v2
Substituting the known values:
-120.0 kg·m/s = (3.00 kg)(vf) + (5.00 kg)(-12.0 m/s)
Solving for vf:
vf = (-120.0 kg·m/s - (-60.0 kg·m/s)) / 3.00 kg
vf = (-120.0 kg·m/s + 60.0 kg·m/s) / 3.00 kg
vf = -60.0 kg·m/s / 3.00 kg
vf = -20.0 m/s
Therefore, the velocity of the 3.00-kg object after the collision is 20.0 m/s west.