RELATIVE MOTION wooden boxcar, sniper, bullets oh my

In summary, a wooden boxcar is moving at speed v1 on a straight railroad track. A sniper fires a bullet with initial speed v2 at the boxcar from a high powered rifle. The bullet passes through both walls of the car, with its entrance and exit holes being exactly opposite each other as viewed from within the car. To determine the direction from which the bullet was fired, we use the Pythagorean theorem and subtract from 180 degrees. This is because the bullet is fired at an angle perpendicular to the track, and the hypotenuse of the triangle represents the speed of the bullet as it leaves the boxcar. We also take into account that the bullet's speed is decreased by 20%.
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Homework Statement



A wooden boxcar is moving along a straight railroad track at speed v1. A sniper fires a bullet (initial speed v2) at it from a high powered rifle. The bullet passes thought both lengthwise walls of the car, its entrance and exit holes being exactly opposite each other as viewed from within the car. From what direction, relative to the track, is the bullet fired from? Assume that the bullet is not deflected upon entering the car, but that its speed is decreased by 20%. Take v1 to be 85 km/h and v2 = 650 m/s.

Homework Equations



3eca9149-c5a9-457f-ab77-365aa4d7a3d5.jpe


The Attempt at a Solution



I don't understand what is going on. Can someone please explain the explanation to me. For example, why is the triangle set up as it is. Why is the hypotenuse the speed of the bullet as it is leaving the boxcar? And why do we have to subtract from 180 degrees.
 
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  • #2
I understand that the bullet is fired from an angle that is perpendicular to the track, but I don't understand why we have to use the Pythagorean theorem and why we are subtracting from 180 degrees. Can someone please explain this to me. Thanks!
 

1. How does relative motion affect the trajectory of a bullet fired from a sniper rifle?

Relative motion is the movement of an object in relation to another object. In the case of a bullet fired from a sniper rifle, the relative motion is affected by factors such as the velocity of the bullet, the direction and speed of the wind, and the distance between the shooter and the target. These factors can cause the bullet to deviate from its intended path, making it more difficult for the sniper to hit their target accurately.

2. Can the shape and material of a wooden boxcar affect its relative motion when in motion?

Yes, the shape and material of a wooden boxcar can affect its relative motion. The shape of the boxcar can impact its aerodynamics, causing it to experience air resistance and alter its velocity. The material of the boxcar can also affect its weight and therefore its acceleration and speed. Additionally, the material can impact the boxcar's ability to withstand external forces, such as friction and collisions, which can change its relative motion.

3. How do external forces, such as friction, impact the relative motion of a wooden boxcar?

External forces, such as friction, can impact the relative motion of a wooden boxcar in several ways. Friction can slow down the boxcar, affecting its speed and potentially causing it to come to a stop. It can also cause the boxcar to change direction, as friction acts in the opposite direction of motion. Furthermore, friction can cause wear and tear on the boxcar, altering its shape and potentially impacting its overall motion.

4. How does the concept of relative motion apply to the movement of a sniper aiming at a moving target?

The concept of relative motion applies to the movement of a sniper aiming at a moving target in several ways. Firstly, the sniper must take into account their own motion, as well as the target's motion, to accurately aim and hit the target. Secondly, the relative motion of external factors, such as wind and distance, must also be considered in order to adjust the trajectory of the bullet. Lastly, the relative motion of the sniper's body, including their breathing and heartbeat, can also affect their aim and must be controlled for an accurate shot.

5. How can understanding relative motion be beneficial in forensic investigations involving wooden boxcars and sniper rifles?

Understanding relative motion can be beneficial in forensic investigations involving wooden boxcars and sniper rifles in multiple ways. For example, it can help investigators determine the trajectory of a bullet and identify potential factors that may have affected its path. It can also assist in reconstructing the sequence of events leading up to a crime scene, as well as identifying potential suspects based on their knowledge and use of relative motion. Additionally, understanding relative motion can aid in determining the cause and effect of collisions involving wooden boxcars and other objects, providing valuable evidence in forensic investigations.

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