Question

The speed of a moving bullet can be deter-

Answer 1

Answer:

$v=16.806\ m/s$

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 $\theta$ it makes in a certain time t, the angular speed is

$\displaystyle w=\frac{\theta}{t}$

If we wanted to know the time it takes to describe some angle, we solve for t

$\displaystyle t=\frac{\theta}{w}..........[1]$

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

$\displaystyle v=\frac{x}{t}.............[2]$

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]

$\displaystyle v=\frac{x}{\frac{\theta}{w}}$

$\displaystyle v=\frac{xw}{\theta}$

We have the values

$\theta=13.7^o=13.7/(2\pi)=2.18\ rad$

$w=432\ rev/min=432*2\pi /60=45.239\ rad/s$

Thus

$\displaystyle v=\frac{(0.81)(45.239)}{2.18}$

$\boxed{v=16.806\ m/s}$