Interpolate between 2 impact points only given the throw angles

In summary, the conversation discusses a problem involving unknowns and the use of a linear function to solve it. The concept of horizontal and vertical angles is also mentioned, with horizontal referring to the tilt of a cannon and vertical referring to its rotation. P3 is related to P1 and P2 as it sits on the line drawn between them. The conversation ends with a request to write expressions for target coordinates using velocity and angles.
  • #1
Werther
3
0
Homework Statement
A cannon shoots at target P1 and P2 with the given vertical/horizontal angles (α/b). But there is a third target (P3) left that is between P1 and P2. Unfortunately the soldier that shoots the cannon only knows the vertical angle (a3=65°) and not the horizontal angle. Notice that the velocity of the projectile and the position of the impact points are unknown.

What is the horizontal angle for shooting at P3 (b3)?
Relevant Equations
projectile velocity:
Vx = cos b * Vc
Vy = sin b * Vc

impact location:
x = Vx*t
Top-Down-Perspective:
Pm (1).jpg


At first I am quite sure that the problem is not solvable since there are that many unknowns.
But my Approach would be to create a linear function with P1 and P2 and then set it equal to the function that gets me the impact location of P3 and then solve it by b3.

Thanks for the help in advance.
 
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  • #2
What are "horizontal" and "vertical" angles?
 
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  • #3
PeroK said:
What are "horizontal" and "vertical" angles?
horizontal = tilt of the cannon
vertical = rotating the cannon left or right
 
  • #4
Okay, and how is P3 related to P1 and P2?
 
  • #5
Werther said:
horizontal = tilt of the cannon
vertical = rotating the cannon left or right
Really? Sounds backwards to me, but from the values given that must be right.

"that is between P1 and P2"
Merely somewhere between, or on the straight line joining them?
 
Last edited:
  • #6
PeroK said:
Okay, and how is P3 related to P1 and P2?
P3 sits in the line If you would draw one through P1 and P2.
 
  • #7
Let the muzzle velocity be v.
Write expressions for the target coordinates in terms of v and the two angles.
 

What is interpolation?

Interpolation is a method used to estimate values between two known data points. It involves using mathematical techniques to fill in the gaps between the data points and create a smooth curve or line.

Why is interpolation useful for analyzing impact points?

Interpolation can be useful for analyzing impact points because it allows us to estimate the location of the impact point between two known points, even if we do not have the exact data for that specific point. This can help us better understand the trajectory and behavior of objects in motion.

What are the factors that affect the accuracy of interpolation for impact points?

The accuracy of interpolation for impact points can be affected by various factors such as the number and spacing of the known data points, the type of interpolation method used, and the quality of the data itself. Additionally, external factors such as air resistance and wind can also impact the accuracy of the interpolation.

What are the common interpolation methods used for analyzing impact points?

Some common interpolation methods used for analyzing impact points include linear interpolation, polynomial interpolation, and spline interpolation. Each method has its own advantages and limitations, and the choice of method depends on the specific data and analysis needs.

How can interpolation be used to improve the accuracy of impact point predictions?

Interpolation can be used to improve the accuracy of impact point predictions by filling in the gaps between known data points and creating a more complete and continuous trajectory. This can help to minimize errors and provide a more precise estimate of the impact point location.

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