x = x0 + v0x t
t = (x – x0)/v0x
y = y0 + v0y t + 1/2 g t^2
y = y0 + v0y (x – x0)/v0x + 1/2 g (x – x0)^2 / v0x^2
y = y0 + v0y/v0x x – v0y/v0x x0 + 1/2 g x^2/v0x^2 – 1/2 g 2 x x0/v0x^2 + 1/2 g x0^2/v0x^2
y = (1/2 g/v0x^2) x^2 + (v0y/v0x – g x0/v0x^2) x + (y0 – v0y/v0x x0 + 1/2 g x0^2 / v0x^2)
y = a x^2 + b x + c
a = 13,92
b = -1,961
c = 0,169
g = 9,8
13,92 = 1/2 g/v0x^2
-1,961 = v0y/v0x – g x0/v0x^2
y0 = 0
0,169 = v0y/v0x x0 + 1/2 g x0^2 / v0x^2
Sistema da risolvere
13,92 = 1/2 g/v0x^2
-1,961 = v0y/v0x – g x0/v0x^2
0,169 = v0y/v0x x0 + 1/2 g x0^2 / v0x^2
Ricavare: v0x, v0y, x0