# Angle of Bullet Fired: Solving for the Initial Angle

• Physics08
In summary, the question asks for the angle at which a bullet was fired from a gun, given its initial velocity of 300 m/s and its time of flight of 3 seconds. To find the angle, the formula V(y-final) = V(y-initial) + a(y)t can be used, where the initial vertical velocity can be found by using the known acceleration of 9.8 m/s^2 and the flight time. However, since the initial vertical velocity is not given, the angle cannot be determined.
Physics08
Hi,

Could somebody please tell me what formula(s) to use to find the answer to the following problem?

A bullet is fired from a gun at 300 m/s. It hits the ground 3s later. At what angle (in degrees) above the horizon was the bullet fired? (Assume no air resistance)

well you have velocity and a time. Think about breaking things up in the x and y components.

In this case, does the x component of velocity ever change?

The Y component of your velocity changes and it changes at a rate of 9.8m/s^2

Since its constant acceleration, use a constant acceleration equation that relates the time, starting velocity, final velocity, and acceleration

OK, how 'bout this?

V(y-final) = V(y-initial) + a(y)t

V(y-final) = -9.8m/s^2 * 3

V(y-final) = -29.4 m/s

then find angle using inverse tangent

Angle = tan-1 (-29.4/300)

Angle = -5.52

Is this correct?

Let me know if I understand the question correctly. Your gun is set on the ground and mounted at an angle that you need to find. The bullet is shot out at 300 m/s and stays in the air for 3 seconds.

If that is the case, is your initial y velocity correct?

here's a question to ask based on the work you just did, is the initial y-velocity zero? Do you know the initial y-velocity?

I assume the initial y-velocity is zero.

No other informtation other than what has been posted is given for the problem

Did I use the correct formula?

Can you let me know if my interpretation of the question is correct? If so, that would mean the bullet was shot out at some initial velocity, which it is true you don't know. However, because you know the acceleration acting on the bullet (9.8 m/s^2) at every point during its flight, and you know how long it stays in the air, those two things tell you exactly what vertical velocity the bullet needs to start off with.

If you can find that initial vertical velocity, and you know the total beginning velocity, which is 300 m/s, you can find the angle.

It's obvious that no one is able to solve this problem because they only ask questions (that lead nowhere) and all the information to the problem has been posted. Thank you all for your help anyway.

## 1. What is the angle of a bullet when it is fired?

The angle of a bullet when it is fired is typically between 0 and 5 degrees from the horizontal. This angle, known as the "angle of departure", is influenced by factors such as the muzzle velocity, wind, and gravity.

## 2. How does the angle of a bullet affect its trajectory?

The angle of a bullet has a significant impact on its trajectory. A bullet fired at a low angle will have a flatter trajectory and travel further before hitting the ground, while a bullet fired at a higher angle will have a steeper trajectory and travel a shorter distance.

## 3. Can the angle of a bullet be adjusted?

Yes, the angle of a bullet can be adjusted by changing the elevation of the firearm. This can be done manually by the shooter or automatically by certain firearms with adjustable sights.

## 4. What is the optimal angle for firing a bullet?

The optimal angle for firing a bullet depends on the specific firearm and ammunition being used, as well as factors such as the distance to the target and environmental conditions. In general, a slightly elevated angle of departure (around 2-3 degrees) is often considered optimal for long-range shooting.

## 5. How does the angle of a bullet affect its impact on a target?

The angle of a bullet can greatly impact its impact on a target. A bullet fired at a low angle may cause minimal damage or pass through the target without stopping, while a bullet fired at a higher angle will have a greater chance of hitting vital organs or causing significant damage upon impact.

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