Galilei and Speed: Solving a Cat and Object Problem

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The problem involves a cat climbing a 3-meter vertical ladder at a constant speed of 4 m/s while an object is thrown from the ground with a gravitational acceleration of 10 m/s². The goal is to determine the initial speed of the object so that it meets the cat exactly once. The discussion includes attempts to apply Galilean equations to find the solution, emphasizing the need for a numerical answer based on the given values. The participants suggest refining the calculations and ensuring all relevant equations are utilized correctly. Ultimately, the focus is on accurately determining the initial speed of the object for the scenario described.
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Homework Statement

"A cat is climbing a vertical ladder from h=3m with the constant speed of v=4m/s. At the same time from the ground it's thrown in the air an object (small dimension) g=10m/s2. Find out the initial speed of the object knowing that it will meet with the cat a single time. (vo=?)

Homework Equations



y1=y2
va + a(t-to)-va root 2+2a(x-xo)

3. The Attempt at a Solution First attempt: http://imgur.com/h84NXzO,B73etyF + drawing second image

I need to find out 2 with the Galilei equation and the speed one
 
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Looks correct, but I think you should add a numerical answer as you got values for v and h.
 

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