I have the following problem:
An airplane P, flying at a height of $h$ needs to hit the target on the ground $T$. The airplane is flying horizontaly at a constant speed $V_0$.
Find the Cauchy problem that $x()$ and $y()$ must satisfy, knowing that only gravity acts on the projectile.
At what distance $x^*$ must the projectile be launched in order to hit the target? After what amount of time $t^*$ will the projectile hit the target?
I know a little about projectile motion and I am very confused at the part where the Cauchy problem is asked? What is that asking? Is it asking to separate the horizontal and vertical movement in two function $x$ and $y$ ? I don't want you to solve my problem for me but any hint would be very muh appreciated. Thank you!