Bullet passing through two holes

[physics10189]

Homework Statement

so this is a classic problem...if you know what i mean.

The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance .082m apart on the sam axle. from the angular displacement 24.9 degree of the two bullet holes in the disks and the rotational speed 819rev/min of the disks.
What is the speed of the bullet. in m/s^2

Homework Equations

The Attempt at a Solution

I try to find time from the starting point of the bullet till the second hole

time=(distance*2pi)/(full revolution of the disk*the degree)
then use that time and put it in the equation of
x final= velocity initial*time.

but didnt get it so any suggestion?

 

[tjr39]

First you should change the rotational speed into usefull units ie radians or degrees per second

Second, you need to use the angular displacement and the rotational speed to find the time it took for the bullet to pass from first to second piece of paper.

Third you will need to use this time and then the distance between the bits of paper to calculate the speed of the bullet. Done!

 

[nlightner]

I would approach this problem by first identifying the known variables and equations that can be used to solve for the unknown variable, which in this case is the speed of the bullet. The known variables are the distance between the two holes (0.082m), the angular displacement of the two holes (24.9 degrees), and the rotational speed of the disks (819 rev/min or 13.65 rev/s).

The first step would be to convert the rotational speed from revolutions per minute to revolutions per second, as this is the unit used in the equation for angular displacement (θ = ωt). This would give us a rotational speed of 13.65 rev/s.

Next, we can use the equation for angular displacement to solve for the time it takes for the bullet to pass through the two holes. Rearranging the equation, we get t = θ/ω. Plugging in the values for the angular displacement (24.9 degrees) and the rotational speed (13.65 rev/s), we get a time of 1.83 seconds.

Finally, we can use the equation for average speed (v = d/t) to solve for the speed of the bullet. Plugging in the distance between the two holes (0.082m) and the time it takes for the bullet to pass through them (1.83 seconds), we get a speed of approximately 0.045 m/s.

In conclusion, the speed of the bullet passing through the two holes is approximately 0.045 m/s. It is important to note that this is the average speed of the bullet, as it is not a constant velocity and may have accelerated or decelerated during its trajectory through the holes.