Question

The speed of a moving bullet can be deter-

Answer 1

Answer:

v = 381 m/s

Explanation:

Linear Speed

The linear speed of the bullet is calculated by the formula:

$\displaystyle v=\frac{x}{t}$

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:

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

Where θ is the angular displacement and t is the time. Solving for t:

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

The angular displacement is θ=14°. Converting to radians:

$\theta=14*\pi/180=0.2443\ rad$

The angular speed is w=1436 rev/min. Converting to rad/s:

$\omega = 1436*2\pi/60=150.3776\ rad/s$

Thus the time is:

$\displaystyle t=\frac{0.2443\ rad}{150.3776\ rad/s}$

t = 0.0016 s

Thus the speed of the bullet is:

$\displaystyle v=\frac{0.61}{0.0016}$

v = 381 m/s