Projectile motion - limited given data

[Crilico]

Homework Statement

Basically, there is a projectile shot from a cannon. When shot, the projectile passes over a net, just barely, which is placed 6.0m away from the cannon, horizontally. The cannon is angled at 40 degrees above the x-axis.

The problem is asking for the muzzle speed of the cannon and how high the net is.

Homework Equations

delta x = .5(Vf + Vi)t
Vf=at + Vi
delta x = .5at^2 + Vit
Vicos40 = X component Vi
Visin40 = Y component Vi

The Attempt at a Solution

I know that delta x would be the 6.0m, X component acceleration is 0, and Y component acceleration is -9.8m/s^2. The problem i am running into is working with the limited number of givens here. I know i need to solve for the time it takes to travel to the net(6.0m horizontally). I'm sure it will involve several equations and substitutions to solve for algebraically(we are using non-calc methods in the course), but I'm not sure where to go with this problem.

 

[Kurdt]

I'd solve for muzzle speed first. you have the correct equations for the components of speed. Now you need to set up two equations of motion. The y-component should be set up for speed and the x component for distance. Now you know that at 6m in the x direction the y-component of velocity will be zero. You can rearrange these two equations to find the initial speed. Finding the height of the net from here should be simple.

 

[denverdoc]

what you do know is that at some unknown t, just as the ball misses the net,

t=6m/Vo*cos40

and Yo=Vo*sin40-.5at^2. Also tan 40=yo/6. Is that enough to do it?