Answer:
[tex]v=16.806\ m/s[/tex]
Explanation:
Rotational Motion
An object is said to have rotational motion is it moves at the same distance to a fixed point called the center. The distance is called radio and the number of revolutions (or radians) it makes over time is called angular speed. Knowing the angle [tex]\theta[/tex] it makes in a certain time t, the angular speed is
[tex]\displaystyle w=\frac{\theta}{t}[/tex]
If we wanted to know the time it takes to describe some angle, we solve for t
[tex]\displaystyle t=\frac{\theta}{w}..........[1][/tex]
Two rotating paper disks are mounted at a distance of x= 81 cm = 0.81 m. If we knew the time the bullet take from one to the other, we could determine the speed of the bullet
[tex]\displaystyle v=\frac{x}{t}.............[2][/tex]
We can determine the time taken between the disks knowing their angular speed and the angle formed in the interval. Replacing the time from [1] into [2]
[tex]\displaystyle v=\frac{x}{\frac{\theta}{w}}[/tex]
[tex]\displaystyle v=\frac{xw}{\theta}[/tex]
We have the values
[tex]\theta=13.7^o=13.7/(2\pi)=2.18\ rad[/tex]
[tex]w=432\ rev/min=432*2\pi /60=45.239\ rad/s[/tex]
Thus
[tex]\displaystyle v=\frac{(0.81)(45.239)}{2.18}[/tex]
[tex]\boxed{v=16.806\ m/s}[/tex]
