- #1
ozzy
- 12
- 0
Well, I am sorry to bother you again, but it seems that after solving my last problem nobody enters that topic anymore I hope I won't get on moderators nerves here...
Well, anyway. As one may remember, I asked about this question:
an aircraft flights at height H with a constant velocity U.
When it passes right above the missile, the missile is fired with a constant velocity V (V>U), but the vector of the velocity of the missile points directly to the aircraft all the time of the flight of the missile.
The question is - what is the time of the total flight of the missile, till it gets the aircraft?
The solution should be done without any integrals.
The solution was made by balakrishnan_v, and did I mentioned that he is THE KING?
But since then I was thinking about the solution and here what I discovered:
the relative velocity between the missile and the plane in Cartesian axis is:
Vx(t) = V*cos{f(t)} - U
Vy(t) = V*sin{f(t)} - 0
and initial position,that should preserve is R = (0 , H)
therefore:
[tex]\int_{0}^{T} (Vcos{f(t)} - U)dt = 0[/tex]
and [tex]\int_{0}^{T} (Vsin{f(t)})dt = H[/tex]
therefore [tex]\int_{0}^{T} (sin{f(t)})dt = H/V[/tex] - which is turns to be right, as checked it in MATLAB.
Though, in the axis system of the missile we get:
the relative velocity between the missile and the plane in missile axis is:
Vs(t) = V - U*cos{f(t)}
Vp(t) = 0 - (-U*sin{f(t)})
and initial position,that should preserve is R = (H , 0)
therefore:
[tex]\int_{0}^{T} (V - Ucos{f(t)})dt = H[/tex]
and [tex]\int_{0}^{T} (Usin{f(t)})dt = 0[/tex]
therefore [tex]\int_{0}^{T} (sin{f(t)})dt = 0[/tex] - Where Am I Wrong? Please help!
Well, anyway. As one may remember, I asked about this question:
an aircraft flights at height H with a constant velocity U.
When it passes right above the missile, the missile is fired with a constant velocity V (V>U), but the vector of the velocity of the missile points directly to the aircraft all the time of the flight of the missile.
The question is - what is the time of the total flight of the missile, till it gets the aircraft?
The solution should be done without any integrals.
The solution was made by balakrishnan_v, and did I mentioned that he is THE KING?
But since then I was thinking about the solution and here what I discovered:
the relative velocity between the missile and the plane in Cartesian axis is:
Vx(t) = V*cos{f(t)} - U
Vy(t) = V*sin{f(t)} - 0
and initial position,that should preserve is R = (0 , H)
therefore:
[tex]\int_{0}^{T} (Vcos{f(t)} - U)dt = 0[/tex]
and [tex]\int_{0}^{T} (Vsin{f(t)})dt = H[/tex]
therefore [tex]\int_{0}^{T} (sin{f(t)})dt = H/V[/tex] - which is turns to be right, as checked it in MATLAB.
Though, in the axis system of the missile we get:
the relative velocity between the missile and the plane in missile axis is:
Vs(t) = V - U*cos{f(t)}
Vp(t) = 0 - (-U*sin{f(t)})
and initial position,that should preserve is R = (H , 0)
therefore:
[tex]\int_{0}^{T} (V - Ucos{f(t)})dt = H[/tex]
and [tex]\int_{0}^{T} (Usin{f(t)})dt = 0[/tex]
therefore [tex]\int_{0}^{T} (sin{f(t)})dt = 0[/tex] - Where Am I Wrong? Please help!