To determine the direction from which the bullet was fired relative to the track, we need to analyze the situation using some basic principles of physics, particularly the concepts of relative motion and velocity. Let's break this down step by step.
Understanding the Scenario
We have a wooden boxcar moving at a speed of 85 km/h along a straight railroad track. A bullet is fired inside the boxcar, passing through both walls, with its entrance and exit holes aligned perfectly. The bullet's speed decreases by 20% upon entering the boxcar.
Calculating the Bullet's Speed Inside the Boxcar
First, let's calculate the speed of the bullet after it enters the boxcar. If we assume the bullet was initially fired at a speed \( v \), then after entering the boxcar, its speed becomes:
- Speed after entering = \( v - 0.2v = 0.8v \)
This means the bullet retains 80% of its original speed after entering the boxcar.
Relative Motion Analysis
Next, we need to consider the relative motion between the bullet and the boxcar. Since the boxcar is moving at 85 km/h, we can express the bullet's speed relative to the ground. If the bullet is fired in the same direction as the boxcar's motion, its effective speed relative to the ground would be:
- Effective speed = \( 0.8v + 85 \) km/h
Conversely, if the bullet is fired in the opposite direction, its effective speed would be:
- Effective speed = \( 85 - 0.8v \) km/h
Determining the Direction of the Bullet
Now, since the bullet passes through both walls of the boxcar and the holes are aligned, it indicates that the bullet's path is straight and not deflected. For the bullet to exit the opposite wall directly across from where it entered, it must have been fired in a direction that compensates for the boxcar's motion.
If the bullet were fired in the same direction as the boxcar's movement, it would exit the wall behind the entry point due to the boxcar's forward motion. Therefore, the only way for the bullet to exit directly opposite its entry point is if it was fired in the opposite direction to the boxcar's motion.
Conclusion
Thus, the bullet was fired from the rear of the boxcar towards the front, relative to the track. This ensures that as the boxcar moves forward, the bullet travels in the opposite direction, allowing it to exit through the wall directly opposite its entry point. This analysis highlights the importance of understanding relative motion in physics, especially in scenarios involving moving frames of reference.
