# Thread: PURSUIT CURVE (differential geom)

1. ## PURSUIT CURVE (differential geom)

I have here a problem in my Diff. Geom class.
----> Suppose an enemy plane begins at (0,0) and travels up the y-axis at constant speed$\displaystyle v_{p}.$ A missile is fired at (a,0) with speed $\displaystyle v_{m}$ and the missile has a heat sensor which always directs it toward the plane.
1.] Show that the pusuit curve which the missile follows is given implicitly by the differential-integral equation
$\displaystyle y=xy^{'}+ \frac{v_{p}}{v_{m}} \int \sqrt{1+y^{' 2}}dx$
2.] Differentiate this expression to get a separable diff. eq. Integate to get the closed form expression fo the pusuit cuve
$\displaystyle y= \frac{a^{\frac{v_{p}}{v_{m}}}}{2(1-\frac{v_{p}}{v_{m}})} [x^{1-\frac{v_{p}}{v_{m}}}-\frac{v_{p}}{v_{m}} a^{1-\frac{v_{p}}{v_{m}}}] - \frac{a^{-\frac{v_{p}}{v_{m}}}}{2(1+\frac{v_{p}}{v_{m}})} [x^{1+\frac{v_{p}}{v_{m}}}+\frac{v_{p}}{v_{m}} a^{1+\frac{v_{p}}{v_{m}}}]$

I already finished no.1. I did no.2 but I got a slightly different answer from the right hand side of the eq. there. Can someone help me out?

2. I cannot answer this question, as it goes against my pacifist beliefs.