what is the equation for projectile motion given an elevated starting point?

write the x and y equations of motion:

x(t) = v0 cos(theta) t

y(t)=y0 + v0y sin(theta) t - 1/2 g t^2

from the x equation, solve for t: t = x/v0 cos(theta)

substitute this into y:

y(x) = y0 + v0y sin(theta)(x/v0cos(theta) - g (x/v0 cos(theta))^2 /2

y(x) = y0 + x tan(theta) - g x^2/(2 v0^2 cos^2(theta))

y0=initial height

v0=initial velocity

theta = launch angle

g=accel due to gravity

As a function of time t since launch, y(t) = h + Uy t - 1/2 g t^2 and x(t) = Ux t; where

h = 50 m above the impact elevation y(T) = 0 and t = T is total time of flight. Uy = U sin(theta) and Ux = U cos(theta), where theta is the angle of launch and U is the initial speed. of launch.

You find total flight time T by solving the quadratic y(T) = 0 = h + Uy T - 1/2 g T^2 assuming the target is at y(T) = 0 height.