Drone $"$A$"$ is flying with constant speed $"$U$"$ along the straigh line, characterised with constant distance $"$H$"$ from this surface.

Angle of inclination of the surface "theta" is known.

Orthogonal projection of the drone $"$A$"$ on the surface is denoted as $"$B$"($i$.$e$.$ AB$=$H$).$

When drone is discovered by the drone distroyer $"$P$",$ the drone is locatated uphill at the distance $"$D$"$ from the point $"$B$"($i$.$e$.$ PD$=$D$)$ and this time is assumed to be zero.

Some time later, at the proper time, projectile is launched towards the drone at angle "beta" relative to the inclined ground surface, as shown in the Figure.

$$ Determine this time $[$in seconds$]$ of the launch of the projectile $($measured from the discovery of drone$),$ enabling intercept of the drone at Point$-2,$ as per the Figure.

Assume NO air resistance.

Also, assume the following parameters:

$$ velocity of the drone U$=44[$m$/$s$]$

$$ initial velocity of the projectile v$0=100[$m$/$s$]$

$$ inclination angle of the ground surface theta$=15[$deg$]$

$$ projectile shooting angle in the inclined coordinates beta$=55[$deg$]$

$$ hight level of the trajectory of the drone AB$=$H$=200[$m$]$

$$ distance from projectile launcher $"$P$"$ to the point $"$B$"($being orthogonal projection of the drone $"$A$"$ on the ground surface$)$ PB$=$D$=1,800[$m$]$

$$ intercept Point: number $2($i$.$e$.$ point with larger projectile flight time to intercept$)$

Recommendation: you may wish to consider using inclined coordinates $($h$\_$bar, z$\_$bar$)$ to formulate differential equations of motion of the projectile and solving them using MATLAB's ODE solver.Figure$-4$: Projectile intercepting drone: notations. $($Not to scale$).$

Projectile $"P,$ Intercepting Drone $"A"$ at Point$-2$