# Bullet trajectory: Aiming a gun

• donaldparida
In summary, the conversation discusses the optimal height at which a person should aim their gun in order to hit a bird from a horizontal distance of 100m, given that the gun imparts a speed of 500m/s to the bullet. The equations used to solve for this height are the maximum height formula and the range formula. The final answer should be 20m, but there is a discrepancy in the diagram and the point at which the gun should be aimed.
donaldparida

## Homework Statement

:
[/B]A person aims a gun at a bird from a point at a horizontal distance of 100m. If the gun can impart a speed of 500m/s to the bullet , then above what height of the bird he should aim his gun to hit it ?

## Homework Equations

: [/B]
$H_{max}=\frac{u^2\sin^2\theta}{2g}$
$R=\frac{u^2\sin2\theta}{g}$
3. The Attempt at a Solution :

Range= $R=\frac{u^2\sin2\theta}{g}$$\implies \sin2\theta=\frac{Rg}{u^2}$$\implies \sin2\theta=\frac{1}{250}$$\implies 2\theta=\sin^{-1}(\frac{1}{250})$$\implies \theta\approx 0.11$Maximum height=$H=\frac{u^2sin^2\theta}{2g}$$\implies H=0.04 m$The correct answer is 20 m. Where have i gone wrong?

Last edited:
donaldparida said:
what height of the bird he should aim his gun to hit it ?
That is not the same as the max height reached. Draw a diagram.

@haruspex, Here is the diagram i drew while solving this problem,

donaldparida said:
@haruspex, Here is the diagram i drew while solving this problem,
View attachment 206195
Ok, so show on it the point above the bird that the person aims at.

donaldparida said:
@haruspex, Why?
If you point a gun in a certain direction, in what direction do you expect the bullet to emerge from the muzzle? What direction is that in your diagram?

The direction of $\vec{U}$?

CWatters
donaldparida said:
The direction of $\vec{U}$?
Yes. So P is a point in that line and vertically above the bird.

## 1. What factors affect the trajectory of a bullet?

The trajectory of a bullet is affected by several factors including the velocity of the bullet, the angle at which the gun is fired, the air resistance, the wind speed and direction, and the gravitational pull.

## 2. How does the distance between the gun and target affect the bullet's trajectory?

The distance between the gun and target has a significant impact on the bullet's trajectory. As the distance increases, the bullet will experience more air resistance, causing it to drop more quickly. This means that the bullet will hit the target at a lower point than the point of aim.

## 3. Is it possible to predict the trajectory of a bullet?

Yes, it is possible to predict the trajectory of a bullet using mathematical equations and computer simulations. These take into account the various factors that affect bullet trajectory and can accurately predict where the bullet will hit the target.

## 4. How does the type of gun affect the bullet's trajectory?

The type of gun can have a significant impact on the bullet's trajectory. Different types of guns have different velocities, barrel lengths, and bullet weights, all of which can affect the trajectory. Additionally, the type of gun can also affect the recoil, which can impact the shooter's ability to aim accurately.

## 5. Can a bullet's trajectory be altered mid-flight?

No, once a bullet has been fired, its trajectory cannot be altered. However, certain factors such as wind speed and direction can affect the path of the bullet. This is why experienced shooters take these factors into account when aiming a gun.

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