y=ft)=(2+01-c0)-3t
Example 1. 12. A projectile is fired with an angle of elevation bo=45 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)=480e-l W e-10)-320 t and a=r(t)=16001-c-10). Since f(8)=8.227andf(9) 320, and its value f(po)=f (8)=-104.3220972 is used in formula(1.40) to get 83.22097200 8.797731010 104.3220972 a summary of the calculation is given in Table 1.4 The value p4 has eight decimal places of accuracy, and the time until impact is tA8.74217466 seconds. The range can now be computed using r(t); and we get r(874217461=16001-c-0812176)=932.4602t
Table 1.4 Finding the Time When the Height f(t) Is Zero k Time, Pk PR+1-Pk Height, f(pk) 080000000797310183.22097200 1|879773101-0.0530160-668369700 2874242941-0.00025475-0.03050700 38.74217467-0.000000-0.00100 48.74217460.00000000
1.4.2 The division-by-Zero Error
1.4.2 The Division-by-Zero Error
Definition 1.4(Order of a root). Assume that f(a) and its derivatives f'(c) f(M(a)are defined and continuous on an interval about x=p. We say that f(ar)=0 has a root of order M at c =p if and only if f(p)=0,f(p),…,f-(p)=0,andf(p)≠0.(153)