Example 1. 12. A projectile is fired with an angle of elevation bo= 450, Wu=Ur= 160ft/sec, and C=10. Find the elapsed time until impact and find the range Using formulas(1.51)and (1.52), the equations of motion are y=f(t)=4800(1 31.534367, we will use the initial guess Po =8. The derivative is f'(t)=480 e-4/10 W e-t10)-320 t and a=r(t)=16001-c-10). Since f(8)=83.22972andf(9) 320, and its value f(po)=f(8)=-104.3220972 is used in formula(1.40)to get 83.22097200 p1 =8.797731010 104.3220972 A summary of the calculation is given in Table 1.4 The value pa has eight decimal places of accuracy, and the time until impact is C8.74217466 seconds. The range can now be computed using r(t); and we get r(8.74217466)=1601-c 0.847217466 =932.4986302ft
Table 1. 4 Finding the Time When the Height f(t)Is Zero k Time, Pk Pk+1-Pk Height, f(pk 0|8.00000797310183.2297200 1|8.7973101-0.05530160-6.68369700 28.74242941-0.00025475-0.03050700 38.74217467-0.0000001-0.000100 48.742174660.00000000000
1.4.2 The division -by- Zero Error Definition 1.4(Order of a Root ). Assume that f(a) and its derivatives f(a) (M) (ar)are defined and continuous on an interval about a= p. We say that f(a)=0 has a root of order M at 2 =p if and only if f(p)=0,f(p), f(-(p)=0,andf(0(p)≠0
1.4.2 The Division-by-Zero Error