Asymmetric initial velocity calculation

[jemerlia]

Homework Statement

A rock is thrown upwards at an angle of 35.0° to the horizontal. The
rock hits a signpost 15.0 m away at a point 2.00 m above the level
from which it was thrown.
Calculate the initial velocity of the rock.

Homework Equations

d = v * t
d= displacement, v=velocity, t=time

x=x0+v0t+1/2gt^2

x= displacement at t
x0 = initial position
v0 = initial velocity
t=time

The Attempt at a Solution

It appears that the x displacement is related:
(1) 15=Vx0 x t

(vx0 is the initial x-component velocity)
because the x velocity is unchanged


The y velocity is related:
(2) 2=vy0t +1/2gt^2

where vy is the initial y vector component

Also:
(3) vx = v0 cos 35
(4) vy = v0 sin 35

It appears possible to substitute for vx, vy so that
15= v0 x cos 35 x t
2= v0 x sin 35 x t + 1/2 gt^2

They look like simultaneous equations but I do not obtain the expected result :(
Help and advice gratefully received.

 

[LowlyPion]

It appears possible to substitute for vx, vy so that
15= v0 x cos 35 x t
2= v0 x sin 35 x t + 1/2 gt^2

Try

15 = V_o*cos35 * t
2 = V_o*sin 35 * t - 1/2 gt²