How Can Numerical Methods in FORTRAN Solve Projectile Motion Problems?

[polka129]

hello people...i have beeen given this projectile problem to be solved numerically in FORTRAN..i have coded it using runge0kutta 4th order ...now the thing is that i have not been given the end points of time,,;ie. the range.. and i am asked to

a)the maximum height attained by the projectile

what is to b added to the existing code to achive this?

b)the time required to reach the maximum height

what is to b added to the existing code to achive this?

c)the time required to return to the original elevation..

what is to b added to the existing code to achive this?

i did fortran 4 years ago...havent beeen in practice..this was the lone effort i cud recall...please help...


i have attached the question and the code..

heres the code
CODE


!**********************************************************************
! *
! projectile question *
! *
!***********************************************************************


DATA M,G,C/10.0,9.80665,0.1/

!FIRST i HAVE REDUCED THE GIVEN EQUATION IN TWO LINEAR 1ST-ORDER EQUATIONS
!FOR THE SOLUTION TO PROCEED


F1(T,U1,Y2) = U1
F2(T,U1,Y2) = (-M*G-C*U1**2)/M


!ASSIGNMENT OF VALUES TO CONSTANTS



WRITE(*,*) 'Input left and right endpoints separated by'
WRITE(*,*) 'blank'
WRITE(*,*) ' '
READ(*,*) A, B

WRITE(*,*) 'Input the two initial conditions.'
WRITE(*,*) ' '
READ(*,*) ALPHA1, ALPHA2

WRITE(6,*) 'Input a positive integer for the number'
WRITE(6,*) 'of subintervals '
WRITE(6,*) ' '
READ(5,*) N


WRITE(*,6)
6 FORMAT(12X,'t(i)',11X,'w1(i)',11X,'w2(i)')

H=(B-A)/N
T=A


! the initiaal conditions
W1=ALPHA1
W2=ALPHA2

WRITE(*,1) T,W1,W2

!RK PARAMETER EVALUATIONS HERE

DO 110 I=1,N

X11=H*F1(T,W1,W2)
X12=H*F2(T,W1,W2)

X21=H*F1(T+H/2,W1+X11/2,W2+X12/2)
X22=H*F2(T+H/2,W1+X11/2,W2+X12/2)

X31=H*F1(T+H/2,W1+X21/2,W2+X22/2)
X32=H*F2(T+H/2,W1+X21/2,W2+X22/2)

X41=H*F1(T+H,W1+X31,W2+X32)
X42=H*F2(T+H,W1+X31,W2+X32)

W1=W1+(X11+2*X21+2*X31+X41)/6
W2=W2+(X12+2*X22+2*X32+X42)/6

T=A+I*H

WRITE(*,1) T,W1,W2
110 CONTINUE


STOP
1 FORMAT(3(1X,E15.8))
END

 

[JaredJames]

Don't use text speak and use code tags in your post with correct indentation to make it easier to read.

So what is your question? We won't solve it for you, only provide you help. I don't see any clear question outlined by yourself. What is it you want help with, the code or the questions?

 

[polka129]

i have attachd the question paper...it is a projectile problem...it has three parts...the answers of which have to b achieved using a numerical method in FORTRAN..i have employed runge-kutta method...i need the fortran commands for these three parts...

i guess the QUESTION is VERY CLEAR...!

 

[JaredJames]

i have attachd the question paper...it is a projectile problem...it has three parts...the answers of which have to b achieved using a numerical method in FORTRAN..i have employed runge-kutta method...i need the fortran commands for these three parts...

i guess the QUESTION is VERY CLEAR...!

So where's your attempt? We're not going to give you the commands without some attempt on your part.

Drop the attitude and the text speak.

 

[rcgldr]

Maximum height is acheived when the projectile transitions from going upwards to downwards. You could optionally use another variable to hold the maximum height, initialize it to the starting height and update it when ever a calculated posiiton is greater.

As far as the end points go, you are given the starting point, and the "endpoint" would occur when the height returned back to it's original value.