Final answer:
To find the original velocity of the bullet, conservation of momentum was applied. The equation used is (Mass of bullet) * (original velocity) = (Mass of bullet + Mass of block) * (Velocity after collision), which yielded a result of 514.29 m/s, albeit not matching any of the options provided.
Step-by-step explanation:
The question involves applying the principle of conservation of momentum to find the original velocity of a bullet before it strikes and becomes embedded in a stationary block. In such a collision, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.
Let's denote the original velocity of the bullet as v. The mass of the bullet is 35 g, which we convert to kilograms by dividing by 1000, giving us 0.035 kg. The mass of the block is 1.8 kg. After the collision, the combined mass of the bullet and block is 1.8 kg + 0.035 kg, which travels at the velocity of 10 m/s. Thus, applying the conservation of momentum:
- Total momentum before = Total momentum after
- (Mass of bullet) * (original velocity of bullet) = (Mass of bullet + Mass of block) * (Velocity after collision)
- 0.035 kg * v = (1.8 kg + 0.035 kg) * 10 m/s
- v = (1.835 kg * 10 m/s) / 0.035 kg
- v = 514.29 m/s
However, this velocity is not one of the provided options, suggesting a possible typo or an oversight in the question itself. The principles used to calculate the answer remain valid, but it is important to ensure the question data is accurate for a meaningful answer.