# Rifle shot and pointed barrel to hit center

• AnkhUNC
In summary, the conversation is about solving a problem involving a rifle that shoots bullets at a high velocity and aiming it at a target a certain distance away. The discussion involves finding the angle at which the gun should be aimed in order to hit dead center on the target, and using trigonometry to calculate the height above the target that the gun should be pointed.
AnkhUNC
[SOLVED] Rifle shot

## Homework Statement

A rifle that shoots bullets at 475 m/s is to be aimed at a target 42.5 m away. If the center of the target is level with the rifle, how high (in cm) above the target must the rifle barrel be pointed so that the bullet hits dead center?

## Homework Equations

sin(2theta) = gd/v0^2

## The Attempt at a Solution

So sin(2theta) = (9.8)*(4250)/(47500^2) = 1.84598338e-5

So sin(2theta) = ?

first calculate how long it would take the bullet to reach the target

then using that time and the Earth's acceleration, calculate how much it must have dropped at the end

this is the height b

a is the horizontal distance
http://em-ntserver.unl.edu/Math/mathweb/trigonom/Image289.gif

calculate the angle

i'm not to sure you can use a right triangle here though, so don't take my word for it :D

Last edited by a moderator:
One needs to work out in cm how high the barrell must be pointed. That means that the gun will be parallel to the ground and all you have to do is work out how far the bullet will deviate vertically due to gravity.

So I have v0, x0 and xF and G. I need to find t in order to find y0 right? I can just assume that the ground is parallel to yF would be 0?

Yes you will need to find t. Just assume the middle of the target is the 0 point for height.

Is there an equation that I don't have to know the angle in order to solve?

Oh sorry I think I mis-read the question. It is asking for the angle I think, but to me its not written very clearly.

So my original answer is right excluding the fact that its wrong?

Your original approach is correct except you seem to be multiplying some of the numbers by 100 for no reason. Once you have the angle you can use trig to find the height above the target centre.

I was doing that so I wouldn't have to convert to cm later on. sin(2theta) = 1.84598338e-5 is right? So how do I just find the angle?

Keep it in meters and convert later. Its not correct because the acceleration due to gravity is in ms-2. Once you have $\sin(2\theta) = ...$ you need to take the inverse sin of the number you get. That will give you twice the angle.

So (-9.8 m/s^2)(42.5)/(475^2m/s) = sin(2theta)? = -.0018459834

Theta = -1.057671168? But that doesn't seem right.

You're a decimal place out and you can lose the minus sign. The angle you have there is twice the angle you want. Remember the bullet travels very fast so the angle will only be small.

So .0018459834 should be .00018459834? /2 = the angle I want?

AnkhUNC said:
So .0018459834 should be .00018459834? /2 = the angle I want?

$\theta$ = 0.106/2. Then one can work out how far above the target the bullet will be aimed through trigonometry.

42.5*tan(.053) = .393135526m = 3.93cm! Thanks!

Sorry for the initial confusion.

## 1. What is the difference between a rifle shot and a pointed barrel?

A rifle shot refers to the act of firing a gun, while a pointed barrel refers to the shape of the barrel of the gun. A pointed barrel is designed to increase accuracy and stability of the shot.

## 2. How does a pointed barrel help in hitting the center?

A pointed barrel helps in hitting the center by providing a more precise and stable path for the bullet to travel. The pointed shape reduces any potential wobbling or deviation of the bullet, increasing the chances of hitting the intended target.

## 3. What factors affect the accuracy of a rifle shot?

Several factors can affect the accuracy of a rifle shot, including the quality of the rifle, the ammunition used, the shooter's skill and experience, weather conditions, and the presence of any external factors such as wind or obstacles in the path of the bullet.

## 4. How can I improve my accuracy when using a rifle?

To improve accuracy when using a rifle, it is essential to practice regularly and become familiar with the weapon. Learning proper shooting techniques, such as proper breathing and stance, can also help. Additionally, using high-quality ammunition and maintaining the rifle in good condition can also contribute to improved accuracy.

## 5. Can a beginner effectively use a rifle to hit the center?

Yes, with proper training and practice, a beginner can effectively use a rifle to hit the center. It is important to start with a suitable rifle and to learn the proper techniques and safety measures before attempting to hit the center. As with any skill, consistent practice is key to improving accuracy with a rifle.

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