Interpolate between 2 impact points only given the throw angles

Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
6 replies · 1K views
Werther
Messages
3
Reaction score
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.
 
Physics news on Phys.org
PeroK said:
What are "horizontal" and "vertical" angles?
horizontal = tilt of the cannon
vertical = rotating the cannon left or right
 
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:
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.