Final answer:
The velocity of the 9-ball after the collision, calculated using the conservation of momentum, is 2.55 m/s.
Step-by-step explanation:
To solve for the velocity of the 9-ball after the collision, we'll use the principle of conservation of momentum. The formula for this says that the total momentum before the collision must equal the total momentum after the collision, given that no external forces are acting on the system.
The equation for momentum (p) is p = m*v, where m is mass and v is velocity. Before the collision, only the cue ball has momentum since the 9-ball is at rest. After the collision, both balls have momentum.
So, the total momentum before the collision equals the mass of the cue ball times its velocity (0.17 kg * 2.9 m/s). The total momentum after collision is the sum of the momentum of both balls, which is (mass of cue ball * its final velocity) + (mass of 9-ball * its final velocity).
Setting these two total momenta equal to each other and solving for the unknown, which is the velocity of the 9-ball after the collision, we find:
0.17 kg * 2.9 m/s = 0.17 kg * 0.5 m/s + 0.16 kg * v (velocity of 9-ball)
0.493 kg*m/s = 0.085 kg*m/s + 0.16 kg * v
v = (0.493 kg*m/s - 0.085 kg*m/s) / 0.16 kg
v = 2.55 m/s