Answer:
v = 381 m/s
Explanation:
Linear Speed
The linear speed of the bullet is calculated by the formula:
[tex]\displaystyle v=\frac{x}{t}[/tex]
Where:
x = Distance traveled
t = Time needed to travel x
We are given the distance the bullet travels x=61 cm = 0.61 m. We need to determine the time the bullet took to make the holes between the two disks.
The formula for the angular speed of a rotating object is:
[tex]\displaystyle \omega=\frac{\theta}{t}[/tex]
Where θ is the angular displacement and t is the time. Solving for t:
[tex]\displaystyle t=\frac{\theta}{\omega}[/tex]
The angular displacement is θ=14°. Converting to radians:
[tex]\theta=14*\pi/180=0.2443\ rad[/tex]
The angular speed is w=1436 rev/min. Converting to rad/s:
[tex]\omega = 1436*2\pi/60=150.3776\ rad/s[/tex]
Thus the time is:
[tex]\displaystyle t=\frac{0.2443\ rad}{150.3776\ rad/s}[/tex]
t = 0.0016 s
Thus the speed of the bullet is:
[tex]\displaystyle v=\frac{0.61}{0.0016}[/tex]
v = 381 m/s
