Object is released at an angle theta with initival velocity v_0. No air resistance. Yes gravity.
v_0x = v_0 * cos(theta) (1)
v_0y = v_0 * sin(theta) (2)
g is gravity
Time it takes to land on the ground:
y(t) = v_0y * t + .5*g*t^2
(When it lands, y(t) = 0)
0 = v_0y * t + .5*g*t^2
0 = t * (v_0y + .5*g*t)
t = 0 (starting point), t = - v_0y / .5*g = -2*v_0y/g (end point)
---
Horizontal displacement: x_t = R
Horizontal velocity at t = {death}: v_x
v_x = R/t
R = v_x * t
R = v_x * {death}
R = v_x*-2*v_0y/g
Since there's no air resistance, v_0x (initial velocity) = v_x (velocity at end time)
R = -2*v_0x*v_0y/g
R = -2 * v*cos(theta) * v*sin(theta)/g (from 1 and 2)
R = -2*v^2 * sin(theta)*cos(theta)/g
sin(2*theta) = 2*sin(theta)*cos(theta) (look it up)
R = -v^2 * sin(2*theta)/g
Since nilson wants initial velocity...
v*2 = -R*g/sin(2*theta)
v = sqrt(-R*g/sin(2*theta))
But there's negatives in the square root!
g = -9.80 m/s^2
v = sqrt(R*9.80/sin(2*theta))
The end.