Projectile Motion - Initial Velocity with Wind

[SomeGuy121]

Hey Physics Forums. This is my first post here, and I'm just wondering about how to find what the initial velocity SHOULD be based on all the other information that I provide (it's for a program application I coded).

Anyways, I have this right now (which is for no wind/0 wind):

I am just wondering how I would go about factoring in the "wind" and wind's angle.

Wind Angles:

^ 90
< 180 > 0
\/ 270

As you can see, the wind angle starts at 0 and moves counter-clockwise.

Anyways, here's the formula:

Velocity = Sqrt((Mass * (DifferenceInX^ 2)) / (2 * (DifferenceInX) * Sin(Theta* PI / 180) * Cos(Thtea * PI / 180) - (2 * (DifferenceInY)) * ((Cos(Theta* PI / 180) ^ 2))))

Where Theta is the angle of the shot; Difference in X is the difference in coordinates X of the starting position and where you want the shot to end; and DifferenceInY is the difference in coordinates Y of the starting and ending position.

Please help me out, thanks.

 

[anathema]

Hi there, welcome to Physics Forums! To find the initial velocity of an object taking into account wind and wind angle, you will need to use vector addition. This means that the initial velocity will be the sum of the velocities in the x and y directions.

To find the x and y velocities, you can use the following equations:

Vx = V0 * cos(theta)
Vy = V0 * sin(theta)

Where V0 is the initial velocity and theta is the angle of the shot.

To factor in the wind, you will need to find the wind velocity in the x and y directions as well. This can be done using the wind speed and angle provided in your formula.

Once you have the wind velocities in the x and y directions, you can add them to the initial velocities in each direction to get the final initial velocity in both the x and y directions.

Here's an example using your formula:

Vx = V0 * cos(theta) + Vwind * cos(wind angle)
Vy = V0 * sin(theta) + Vwind * sin(wind angle)

Where Vwind is the wind velocity and wind angle is the angle of the wind.

Hope this helps! Good luck with your program application.

 

[tomcue]

Hello there! It's great to see someone coding and exploring projectile motion. To factor in wind, you will need to consider the wind's velocity and angle in relation to the projectile's initial velocity. The wind's velocity can be added to the projectile's initial velocity vector, and the wind's angle can be taken into account by adjusting the angle of the initial velocity vector.

To calculate the new initial velocity, you can use vector addition. The magnitude of the initial velocity vector will be the same as the formula you provided, but the angle will need to be adjusted to account for the wind angle. This can be done by using the Law of Cosines or trigonometric functions.

Additionally, you will need to consider the direction of the wind in relation to the projectile's path. If the wind is blowing in the same direction as the projectile, it will increase the initial velocity. If the wind is blowing in the opposite direction, it will decrease the initial velocity.

I would also recommend factoring in air resistance and the projectile's mass to get a more accurate calculation. Overall, the initial velocity will depend on the specific variables and conditions of your program, so it may require some experimentation and fine-tuning. Best of luck with your project!