Projectile height formula based on distance?

In summary, the conversation discusses finding the height and distance of a projectile shot from the ground at a target, using known values for drag, lift, angle, and velocity. The formula involves finding functions for height and distance, and plugging in values to solve for time and ultimately the height at a specified distance from the target. There may be some difficulty with algebra, but the method is feasible.
  • #1
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If a projectile shot from the ground were shot at a target located at a specified height above the ground, and would hit the target, is there a known formula to find the projectile’s height on its trajectory a specified distance (measured along the flat ground) from the target’s base or from the projectile’s launch point (which is on the ground)? I’m hoping for something based on the distance along the ground rather than on time. I have some rough numbers to use for drag and for lift and numbers for angle and velocity. Seems to me the drag and lift would prevent the trajectory from being the same shape on both sides of the trajectory’s highest point. The entire trajectory would occur over a flat surface.
 
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  • #2
So you know trajectory, initial velocity, lift and drag, so you should be able to find h(t) and d(t) where h = height and d = distance. Using these two functions, you can hold t fixed and find t = f(d). Then plug f(d) back into your equation for h(t), giving h(f(d)).
It might get complicated in the algebra, but should not be too hard.
 
  • #3
Thanks. I'll try to give that a try.
 

Related to Projectile height formula based on distance?

1. How do you calculate the height of a projectile based on its distance?

The height of a projectile can be calculated using the formula h = (v02sin2θ)/2g, where h is the height, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

2. What is the significance of the distance in the projectile height formula?

The distance in the projectile height formula represents the horizontal displacement of the projectile. It is used to calculate the time of flight and ultimately, the height of the projectile.

3. Can the projectile height formula be used for any type of projectile motion?

Yes, the projectile height formula can be used for any type of projectile motion, as long as the projectile is launched at an angle and experiences a constant acceleration due to gravity.

4. How does air resistance affect the projectile height formula?

Air resistance can affect the projectile height formula by reducing the maximum height and range of the projectile. This is because air resistance acts as a force opposing the motion of the projectile, causing it to slow down.

5. Is the projectile height formula affected by the mass of the projectile?

No, the projectile height formula is not affected by the mass of the projectile. This is because the formula only takes into account the initial velocity, launch angle, and acceleration due to gravity, which are independent of the mass of the projectile.

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