Projectile Motion with Given Angle and Velocity

In summary, the conversation discusses a problem with finding the equations to solve for the maximum height and time for a bullet shot at an angle with a muzzle velocity of 412 m/s and starting height of 2 meters. The equations needed are y=y0+Y0y\Deltat+1/2(ay)\Deltat2 and range=v0(cos27.2)\Deltat. The answers found so far are a time of 38.4 seconds and a range of 14079.67 meters. The final equations needed are t = Vo*Sinθ/g and Y = 2 + ½gt².
  • #1
roboman32
2
0
I am having a problem with this question. I have it half solved but I cannot figure out what equation I am supposed to use for the rest.

Homework Statement


A hunter shoots his rifle at an angle of 27.2 degree above the horizontal. He is holding the rifle so that the muzzle of the rifle is exactly 2 meters above the ground. The muzzle velocity of the rifle is 412 m/s

The answers needed for this question are the following:
How long is the bullet in the air?
What is the bullet's range?
What is the maximum height of the projectile?
How long does it take the bullet to reach its maximum height?

Starting velocity = 412 m/s
Starting height = 2 meters
Range = 14079.67
change in time = 38.4 seconds

Homework Equations



y=y0+Y0y[tex]\Delta[/tex]t+1/2(ay)[tex]\Delta[/tex]t2
range=v0(cos27.2)[tex]\Delta[/tex]t

The Attempt at a Solution


I have found the answers to the first two answers which are:
How long is the bullet in the air? 38.4 seconds
What is the bullet's range? 14079.67 meters

but I am not sure what equations I am supposed to use for these questions:
What is the maximum height of the projectile?
How long does it take the bullet to reach its maximum height?
 
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  • #2
Welcome to PF.

You can calculate the time to max height easily enough.

Vo*Sinθ = g*t

t = Vo*Sinθ/g

You should know then that Y = 2 + ½gt²
 
  • #3
thank you
 

1. How does the trajectory of a gun affect its accuracy?

The trajectory of a gun refers to the path that the bullet follows once it is fired. It is affected by various factors such as the velocity of the bullet, the angle of the gun, and external forces like wind. The trajectory ultimately determines the accuracy of the gun, as a deviation in the path can result in missing the target.

2. What is the relationship between the muzzle velocity and the trajectory of a gun?

The muzzle velocity, which is the speed at which the bullet leaves the barrel of the gun, has a direct impact on the trajectory. A higher muzzle velocity will result in a flatter trajectory, meaning that the bullet will travel in a straighter line and drop less over a given distance. On the other hand, a lower muzzle velocity will result in a steeper trajectory with more drop over the same distance.

3. How does the angle of the gun affect the trajectory?

The angle of the gun, also known as the elevation angle, plays a crucial role in determining the trajectory of the bullet. A higher angle will result in a longer flight time and a higher point of impact, while a lower angle will result in a shorter flight time and a lower point of impact. The ideal angle for maximum range and accuracy is typically between 30-45 degrees.

4. Can external forces impact the trajectory of a gun?

External forces such as wind, gravity, and air resistance can all affect the trajectory of a gun. Wind can cause the bullet to deviate from its intended path, while gravity pulls the bullet downwards, resulting in a drop in the trajectory. Air resistance can also slow down the bullet, causing it to drop more over a given distance. These factors must be taken into account when aiming and adjusting for the trajectory of a gun.

5. How can I calculate the trajectory of a gun?

To calculate the trajectory of a gun, you will need to know the muzzle velocity, the elevation angle, and the distance to the target. Using these values, you can use mathematical equations such as the projectile motion equation to determine the trajectory of the bullet. There are also various online calculators and apps that can help you calculate the trajectory of a gun based on these factors.

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