math (calculate speed)
posted by AMT .
A swimmer of mass m is at a swimming pool. They climb the steps to the diving board 4.0 m above the water. They jump off the board, which enables them to rise a further 0.7 m before they begin their descent into the pool. At what speed do they enter the water?
You may assume that the acceleration due to gravity, g, is 9.8 m s−2
Show your working step by step, including the correct formulas and equations.

m*g*h = 1/2*m*v^2
where m is the mass; g is the acceleration due to gravity; v is the speed.
At the top of his dive, the swimmers energy is entirely potential energy = m*g*h;
When he enters the pool, the potential energy is converted to kinetic energy: 1/2*m*v^2
v = = (2*g*h)^0.5 
9.6