Find Initial Velocity given angle, distance, height launched from.

[mhsphysics10]

1. A nerf gun in a vacuum is fired from .98 meters at an angle of 15degrees, going 7.86m. Find the initial velocity of the gun, then find the horizontal and vertical components of the initial velocity.

Knowns
g=-9.8m/s²
y_o=.98m
x_o=0m
y=o ( the final height of the dart is 0)
x=7.86m
θ=11 degrees

Homework Equations

x=x_o+v_ot
y=y_o+v_ot+.5gt²
v_ox=v_ocosθ
v_oy=v_osinθ

The Attempt at a Solution

So first i simplified the x equation down to get time on one side to get
(x-x_o)/(v_ocos11)=t
Then i plugged in the numbers to get
{7.86/(v_ocos11)}=t

Then i plugged in the parts for the y equation,
-.98=v_oyt+-4.9t²
Now what do i do? do take out a t and plug in the x equation?

 

[Feldoh]

Why not substitute in v_0* sin (theta) = v_0y. Then you have two equations and two unknowns and from that everything else is easy to find!