Projectile motion with a region of 0 acceleration

[suchara]

Homework Statement

I don't know if the title is misleading or not because I can't think of anything better ..

I need help with something I've been working on... its not homework...its more of a side project/hobby of mine, but i couldn't figure out where to put this question..

Basically I need to figure out the x-component of the initial velocity
So let's call it Vi

Heres the scenario

http://img27.imageshack.us/img27/5536/sce1d.jpg

The known values are
d1= 10
d2= 10
d3= 10
a = 10 during d1 and d3 and a = 0 during d2 (see pic above)
and t1+ t2 + t3 = 3 seconds

Homework Equations

Vf = Vi + a*t
d= Vit + 0.5*a*t^2
d = v*t (if acceleration = 0)
vf^2 = vi^2 + 2ad

So basically I started off with the following 3 equations, I only used the first three equations from above

d1 = Vi*t1 + 0.5*a*t1^2

d2 = V2*t2 (since acceleration = 0)
Since V2 = Vi + at1, then
d2 = (Vi + a*t1)t2 = Vi*t2 + a*t1*t2

d3 = V2*t3 + 0.5*a*t3^2
or in terms of Vi
d3 = Vi*t3+ a*t1*t3 + 0.5*a*t3^2

The Attempt at a Solution

d1+d2+d3= Vi*t1 + 0.5*a*t1^2 + Vi*t2 + a*t1*t2 + Vi*t3+ a*t1*t3 + 0.5*a*t3^2

Then I rearranged the equation to get

dtotal = Vi(t1+t2+t3) + (0.5*a*t1^2 + a*t1*t2 + at*t1*t3 + 0.5*a*t3^2)

Mutiply both sides by 2 to get rid of 0.5

2*dtotal = 2*Vi(t1+t2+t3) + a(t1^2 + 2*t1*t2 + 2*t1*t3 +t3^2)

After plugging in the known values, this is the point I am stuck at

60 = 6*Vi + 10(t1^2 + 2*t1*t2 + 2*t1*t3 +t3^2)

Is there any way I can reduce the above equation knowing t1+t2+t3 = 3 to find out Vi?

Or maybe I am doing this completely wrong and there's a better way to find out Vi given the scenario??

 

[rl.bhat]

I can visualize the problem this way.
A particle is projected with an initial velocity V making an angle of projection theta.When it reaches the maximum height, its velocity is horizontal. It lands on a table of length 10 m with frictionless surface. At the end of the table it travels in the similar way as in the first case with reversed direction.
With these hints try to solve the problem.