How can a traveling bullet be accurately measured?
How can a traveling bullet be accurately measured?
Answer:
In order to measure the velocity of a bullet, and measure the position of it in space at the same time, 2 photogates can not maximize accuracy of both at the same time. An increase in distance between the gates can improve the average velocity, but it will also decrease the accuracy of position. By placing the gates next to each other, the accuracy of knowing the average velocity will decrease due to the ability to measure the position inside the photogates with great accuracy.
In order to improve knowledge of both position of the bullet in space at a give time, and improve knowledge of the velocity (both momentary and average), the solution is to separate the two gates by a large distance, and add more gates at known positions in-between the two original gates. This will allow for the same accuracy of average velocity, or even show the decrease in velocity, as well as allow for accuracy of position due to the reduction of time in-between gates where the velocity and position is not yet known.
The more gates, the better.
Example:
gate1 gate2 >
|___________| Bullet
X
>
|___________| t=ti
>
|___________| t=tf
V = X/t (hence average velocity)
But:
>
|___________|___________|___________|___________|
v1(avg)=x1/t1 v3(avg)=x3/t3
v2(avg)=x2/t2 v4(avg)=x4/t4
...AND...
V = X/t
These average velocities combined will better show de-acceleration.
