Solving the Angle Required to Hit a Moving Target with Ballistic Projectiles

[Jripe]

Say you have a target with a velocity on the x and y-axis and acceleration on the x and y axis.
Now, you have a gun with a fixed muzzle velocity. The gun is being carried by something with a velocity on the x and y and acceleration on the x and y. How would I go about solving the angle required to hit the target at any given time?

The velocities and accelerations are not constant, but can be produced at any given time.

I'm basically looking for a kick in the right direction of the things I will need to know to figure this out.
Thanks.

 

[lpfr]

You say "hit the target at a given time". This means you can know the point of impact (as you know the velocities and accelerations of the target).
You compute the parabola that passes by the impact point (if it exists). This gives you the angle of the muzzle. Then you compute the time for the projectile to reach this point. This allows you to know when to push the button.

 

[charng]

To solve the angle required to hit a moving target with ballistic projectiles, you will need to consider several factors such as the target's position, velocity, and acceleration, as well as the gun's muzzle velocity, and the carrier's velocity and acceleration. This problem can be approached using principles of physics such as projectile motion and relative motion.

First, you will need to determine the initial position and velocity of the target. This can be done by measuring or estimating the target's position at a certain time and calculating its velocity using the change in position over time. Similarly, the carrier's velocity and acceleration can be measured or estimated.

Next, you will need to determine the muzzle velocity of the gun, which is the initial velocity of the projectile when it leaves the gun. This can be measured or calculated based on the gun's specifications.

Using these initial values, you can then use the equations of projectile motion to calculate the trajectory of the projectile. This will involve considering the effects of gravity and air resistance on the projectile's motion. You will also need to take into account the relative motion between the gun and the carrier, as this will affect the projectile's trajectory.

To hit the moving target, you will need to adjust the angle of the gun's barrel to align with the calculated trajectory of the projectile. This can be done by using trigonometric functions to calculate the required angle. It is important to note that this angle will need to be constantly adjusted as the target and carrier's velocities and accelerations change over time.

In summary, to solve the angle required to hit a moving target with ballistic projectiles, you will need to consider the target's position, velocity, and acceleration, as well as the gun's muzzle velocity, and the carrier's velocity and acceleration. You will also need to apply principles of projectile motion and relative motion to calculate the required angle.