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.(adsbygoogle = window.adsbygoogle || []).push({});

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)) whereg(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 equals70t

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))+Con 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.

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# Curve of Pursuit

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