Suppose that a hawk, whose initial position is (a,0)=(3000,0) on the x-axis, spots a pigeon at (0,-1000) on the y-axis. Suppose that the pigeon flies at a constant speed of 60 ft/sec in the direction of the y-axis (oblivious to the hawk), while the hawk flies at a constant speed of 70 ft/sec, always in the direction of the pigeon. All the answers provided are correct, and I'm really close to the end I'm just stuck on one part. The pigeon's position is given by the function (0, g(t)) where g(t)=60t-1000 The hawk's line of travel is tangent to the curve of pursuit, and is given by (1000+y-(x*p))/60 (where p=dy/dx) The distance the hawk has flown is given by the integral ∫[x, 3000] √(1+p^2) which also equals 70t The total distance can be considered: ∫[x, 3000] (1/70)√(1+p^2) Next both sides of the equation are differentiated giving: (-1/60)*(x*q) on the left and (-1/70)(sqrt(1+p^2)) on the right This is now a separable equation with the variables p and x. It can be equated to: (p/sqrt(p^2+1)+1)/(sqrt(p^2+1)+p)=6/(7x) Integrating we get ln(p+sqrt(1+p^2)) on the left and 6/7(ln(x))+C on the right solving for C we get =-6.535150622 and here's where the roadblock comes in. I cannot for the life of me solve for P. Wrong answers I've tried: P=sqrt((e^(6/7(ln(x))-6.535150622)^2-1)/2) a given hint was to "Exponentiate to get rid of the logarithm. Then isolate the square root on one side of the equation and square both sides" which is what I thought I did but I must be doing something wrong. I've been stuck on this for a good 2 hours and have gotten many answers but no success. After solving for P, I have to solve for y, given that P=(dy/dx), then solve for C by plugging in the initial position of the hawk. Any help would be really appreciated. I still have till Monday to have this done but it would be a huge load off my mind to finish it off by tomorrow.