Erupting Volcano Kinematics in 2D problem

[DeltaDeltaDelta]

Ok, I've been working on this for awhile and I can't seem to understand how to work it out. ANY insight would be greatly appreciated!

The problem: An erupting volcano (2.5 km tall) projects a boulder from a vent at an angle of 40 degrees to the horizontal direction. The rock lands 6.0 km away. Introduce an appropriate coordinate system, tailor kinematic equations to the given information and determine the initial speed of the rock and time of flight.

So basically, I'm having a huge mental block trying to figure out the initial velocity. So far I've come up with some answers, but I believe they're incorrect. I took my equation for distance in the horizontal direction S= V(i) * t. and solved for time. You know that the distance in the x direction is 6000 meters. So the Initial velocity in the x direction will be X distance/time. But I didn't know how to find the time, and I was only solving for the x component of initial velocity anyway! Like I said, any thoughts would be helpful because I've been stuck on this for a LONG time, and I've got a midterm coming up where I have to determine the initial velocity of a bullet and accurately fire a metal ball at some predetermined angle directly into the center of a cart some distance away.

 

[Astronuc]

The solution will depend on the elevation of the ground where the boulder lands. If the volcano is 2.5 km tall, does this imply the boulder lands at an elevation 2.5 km below its initial lauch point.

The initial velocity is to be determined from the equations of motion, and the fact that one has a horizontal distance of 6 km.


See - http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra9