# How Can Numerical Methods in FORTRAN Solve Projectile Motion Problems?

• polka129
In summary: When the calculated height is no longer greater than the original height, you know you've returned close enough to the original point. You can also check the derivative of the height to make sure it's 0.The time to reach the maximum height can be found by keeping track of the time when the calculated height is at the maximum height. The time to return to the original elevation can be found by keeping track of the time when the calculated height returns to the original height.
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?

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(*,*) ' '

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

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

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

#### Attachments

• projectile question.png
28.5 KB · Views: 429
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?

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...!

polka129 said:
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.

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.

## 1. Can all scientific problems be numerically solved?

No, not all scientific problems can be numerically solved. Some problems may not have a numerical solution or may require advanced techniques that are not yet developed.

## 2. What types of scientific problems are typically solved numerically?

Scientific problems that involve complex mathematical equations, simulations, or large datasets are typically solved numerically.

## 3. How accurate are numerical solutions compared to analytical solutions?

Numerical solutions can be highly accurate, but they may involve some degree of error due to rounding or approximations. Analytical solutions, on the other hand, are exact and do not involve any error.

## 4. What are some common numerical methods used to solve scientific problems?

Some common numerical methods include finite difference methods, finite element methods, and Monte Carlo simulations.

## 5. How do numerical solutions aid in scientific research?

Numerical solutions allow scientists to model and study complex systems that may be difficult or impossible to study in real-life experiments. They also provide a way to test hypotheses and make predictions about real-world phenomena.

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