Final answer:
The velocity of both the dart, weighing 0.05 kg, and the dartboard, weighing 0.15 kg, after their inelastic collision is 0.3225 m/s, calculated using the conservation of momentum principle.
Step-by-step explanation:
To determine the velocity of the dart and dartboard after the collision, we need to apply the law of conservation of momentum, considering the collision is perfectly inelastic. This means that the dart and the dartboard will move together with the same velocity after the collision.
The formula for conservation of momentum is m1•v1 + m2•v2 = (m1 + m2)•v' where mass times velocity before collision equals the combined mass times shared velocity after the collision.
Let mass of dart (m1) = 0.05 kg with initial velocity (v1) = 1.29 m/s, and mass of dartboard (m2) = 0.15 kg with initial velocity (v2) = 0 m/s (as it is at rest). Plugging in the values, we get:
0.05 kg • 1.29 m/s + 0.15 kg • 0 m/s = (0.05 kg + 0.15 kg) • v'
Solving for v', the shared velocity after collision, gives:
v'=(0.05 kg • 1.29 m/s) / (0.05 kg + 0.15 kg) = 0.3225 m/s
Hence, the velocity of both the dart and the dartboard after the collision is 0.3225 m/s.