A 70 Kg tower diver performs a handstand dive. The distance he falls vertically from the takeoff until his hands first touch the water(entry) is 10m. How fast will he be falling (i.e. vertical velocity) when he hits the water in m/s?

First of all, his mass is irrelevant. Ignoring air resistance, all objects are subject to the same gravitational acceleration, regardless of mass.

Since this is clearly a homework problem, I'll try to get you going in the right direction, but it's up to you to work through the problem.

To figure out how fast the diver is traveling, you first need to find out how much time he spends in the air. You know the distance he falls; you know the acceleration of gravity. What's the formula that relates distance, acceleration, and time?

Once you know the time he spends falling, you just need to apply the formula that gives you velocity as a function of acceleration and time. What's that formula?

And there is one formula that relates the final speed, the initial speed, the acceleration and the distance.

But until you solve this problem by equations you know about, I'll keep it. I want to be sure you understand what you are doing first.