program ex072
c
c     This program solves the equation
c           h = v0**2/g*log(cosh(g*t/v0))
c     by using the Newton's method
      implicit real*8 (a-h,o-z)
      real*8 m			! Declare m is double precision real variable
c
c Statement function
      x(t)= h - v0**2/g*log(cosh(g*t/v0))
      v(t)= - v0*tanh(g*t/v0)
c
      eps = 1.0d-10             ! Allowed Error
      nmax = 100
      h0 = 20.0d0                ! Max. Height
      g = 9.8d0			! Gravitation Acceleration
      gam = 1.0d0		! Friction Constant
      a = 0.035d0		! 3.5 cm (baseball) ??
      m = 0.40d0		! 400 g (baseball) ??
c     a = 0.15d0		! 15 cm (football) ??
c     m = 1.00d0		! 1 kg  (football) ??

c Parameter Inputs
      write(*,800) "# a, m, h, nmax = ?"
      read(*,*) a, m, h0, nmax
      write(*,800) "# a, m, h, nmax =", a, m, h0, nmax
      write(*,800) 
     & "#      h               t               t (no fric.) Steps"
800   format(a,3(1x,f10.5),1x,i5)
c
      dh = h0 / nmax             ! step of h
      v0 = sqrt(m*g/gam/a/a)
c
      t = sqrt(2*dh/g)		! If gam=0, x(t)=g*t**2/2
      do i = 1, nmax
         h = i*dh               ! We study various h
c        t = sqrt(2*h/g)	! If gam=0, x(t)=g*t**2/2
	 n1 = 1
	do n=1,1000
		xt = x(t)
		n1 = n
		if(abs(xt).lt.eps) goto 20
		dt = -xt/v(t)   ! Newton 法
		t = t + dt
	enddo
c
 20      continue 
         write(*,100) h, t, sqrt(2*h/g), n1 ! 最終的な答えを書く
      end do
c
      stop
 100  format(3(1x,f15.7),1x,i4)
      end