Speed of a Bullet: Deriving Formula with D, T & Theta

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    Bullet Speed
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Homework Help Overview

The problem involves deriving a formula for the speed of a bullet in relation to the distance between two disks, the rotational period of the disks, and the angle of penetration. The context is centered around kinematics and rotational motion.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the rotational period and the angle to determine the time it takes for the bullet to traverse the distance between the disks. There is a question about how to calculate the time required for the bullet to cross the gap.

Discussion Status

The discussion is ongoing, with some participants suggesting methods to find the bullet's speed by relating the distance and time. There is an exploration of different interpretations regarding the timing of the bullet's penetration relative to the rotation of the disks.

Contextual Notes

Participants are navigating constraints such as the inability to use the radius in their calculations and the need to derive the formula based solely on the given parameters.

tigerseye
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I've been stuck on this problem forever and I don't know how to do it if you can't use r as the radius.
A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T (see the attached picture). Derive a formula for the bullet speed v in terms of D, T, and a measured angle theta between the position of the hole in the first disk and that of the hole in the second.
 

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You know the time required to make a full revolution and from the angle you can determine the time it takes the bullet to traverse the gap. Find the speed of the bullet by just dividing the length of the gap by the time it takes to cross it.
 
I no this sounds stupid but how do you find how long it takes to cross the gap !
 
If the bullet penetrated the second disk 45^\circ[/tex] later than where it penetrated the first disk, then the disks traveled 1/4 turn in the time it took the bullet to penetrate both disks, so...
 

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