Im doing a problem that is lots of steps to find when this hawk catches this pigeon,
The given information is
The hawk's initial position is (a,0) and is 8000,0 it is moving at constant speed of 50 ft/s
The pigeon's position is (5000,0) and its moving 30 ft/s constant speed.
Ill put in some background of what I have already calculated and know is right (problems are web based so you get to know if your correct right away) Whats in Bold I have got right in the problem set.
The pigeon's position Q=(0,g(t)) is given by the following function of time
Found g(t) to=30t+5000
The fact that the hawk is always headed in the direction of the pigeon means that the line PQ is tangent to the pursuit curve y=f(x). This tells us that {dy}/{dx}=h(x,y,t) where h(x,y,t) =((30t+5000)-y)/(0-x)
If we solve the equation
p = h(x,y,t),
here p={dy}/{dx}, for time we obtain that t=k(x,y,p) where
k(x,y,p)=((-xp)+y-5000)/30
we see that the distance that the hawk has flown in time t is given by the integral from c to d ∫F dx where
C=x
d=8000
F=sqrt(1+p^2)
on the other hand the hawk is flying at a constant speed of 50 for time t. Hence the total distance it has flown is 50t
f we equate this to the distance we just computed and solve for t we obtain
Where G=sqrt(1+p^2)/50
So Im good uptill this point, then the next question things go down hill.
Equating the two expressions for t from Problems 1 and 2 we obtain the integral equation
To get rid of the integral, we differentiate both sides of the equation with respect to x.
On the left hand side of the resulting equation we obtain the following expression....
while on the right hand side (after applying the Fundamental Theorem of Calculus) we obtain....
No matter what I try the computer says im wrong
Any help would be greatly appreciated
Thanks!
If it helps heres the picture of the hawk and pigeon
The given information is
The hawk's initial position is (a,0) and is 8000,0 it is moving at constant speed of 50 ft/s
The pigeon's position is (5000,0) and its moving 30 ft/s constant speed.
Ill put in some background of what I have already calculated and know is right (problems are web based so you get to know if your correct right away) Whats in Bold I have got right in the problem set.
The pigeon's position Q=(0,g(t)) is given by the following function of time
Found g(t) to=30t+5000
The fact that the hawk is always headed in the direction of the pigeon means that the line PQ is tangent to the pursuit curve y=f(x). This tells us that {dy}/{dx}=h(x,y,t) where h(x,y,t) =((30t+5000)-y)/(0-x)
If we solve the equation
p = h(x,y,t),
here p={dy}/{dx}, for time we obtain that t=k(x,y,p) where
k(x,y,p)=((-xp)+y-5000)/30
we see that the distance that the hawk has flown in time t is given by the integral from c to d ∫F dx where
C=x
d=8000
F=sqrt(1+p^2)
on the other hand the hawk is flying at a constant speed of 50 for time t. Hence the total distance it has flown is 50t
f we equate this to the distance we just computed and solve for t we obtain
Where G=sqrt(1+p^2)/50
So Im good uptill this point, then the next question things go down hill.
Equating the two expressions for t from Problems 1 and 2 we obtain the integral equation
To get rid of the integral, we differentiate both sides of the equation with respect to x.
On the left hand side of the resulting equation we obtain the following expression....
while on the right hand side (after applying the Fundamental Theorem of Calculus) we obtain....
No matter what I try the computer says im wrong
Any help would be greatly appreciated
Thanks!
If it helps heres the picture of the hawk and pigeon