Final answer:
To find the velocity of the dart and apple just after the dart is embedded, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision. The velocity of the dart and apple just after the dart is embedded is 2.99 m/s.
Step-by-step explanation:
To find the velocity of the dart and apple just after the dart is embedded, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision. The momentum of an object is defined as the product of its mass and velocity.
Before the collision, the momentum of the dart can be calculated as mass of dart * velocity of dart. After the collision, the combined mass of the dart and apple will be the sum of their individual masses. The velocity of the dart and apple just after the dart is embedded can be calculated by dividing the initial momentum of the dart by the combined mass of the dart and apple.
Let's calculate:
Mass of dart = 46 g = 0.046 kg
Mass of apple = 108 g = 0.108 kg
Velocity of dart = 10 m/s
Combined mass of dart and apple = 0.046 kg + 0.108 kg = 0.154 kg
Momentum before collision = mass of dart * velocity of dart = 0.046 kg * 10 m/s = 0.46 kg*m/s
Velocity of dart and apple just after the dart is embedded = Momentum before collision / Combined mass of dart and apple = 0.46 kg*m/s / 0.154 kg = 2.99 m/s