Final answer:
To solve for the missing initial velocity v1 using the conservation of momentum, we calculate v1 to be approximately 13.33 m/s, given the final velocities are equal for both masses during the collision.
Step-by-step explanation:
The question involves solving for the missing variable in a situation using the conservation of momentum. The details provided allow us to set up the momentum conservation equation, which in simplified terms for an object initially at rest (m2v2 = 0 since v2 before collision is not provided, suggesting it might be zero) is:
m1v1 + m2v2 = m1v'1 + m2v'2
With m1 = 3 kg, m2 = 2 kg, v'1 = 8 m/s, and v'2 = 8 m/s, the initial velocity of the first object (v1) before the collision can be calculated. Since the final velocities of both objects are the same, we can simplify the equation to:
m1v1 = (m1 + m2)v'
Substituting the given values:
(3 kg)v1 = (3 kg + 2 kg)(8 m/s)
v1 = (5 kg)(8 m/s) / (3 kg)
v1 = 40 m/s / 3 kg
v1 =~ 13.33 m/s