Kinematics with multiple objects

[Vontox7]

Homework Statement

Mike is standing below a tower. His friend on top of the tower which is 580 m drops a balloon at him. At the instant mike fires a potato from a cannon moving at an initial velocity of 95 m/s. How long does it take for the balloon and potato to collide?

Homework Equations

vf=vi+at
vf^2=vi^2+2ax
x=vi*t+0.5at^2
x=0.5(vi+vf)t

The Attempt at a Solution

What i did is split it into 2 parts one for the balloon and potato. The potato equation was
x=95t+0.5(-9.81)t^2
And the balloon equation as
x=0.5(9.81)t^2
and then i set them equal to each other and solved.
I got t=9.684 s

 

[Spinnor]

At t = 0 both the potato and balloon are at x = 0 do they both start at the same point? I think you want to measure distances from some common point, either at the bottom of the tower or at the top?