A diver of mass m drops from a board 12 m above the water surface. Calculate his speed 6m above the water surface. What is the speed of the diver just he strikes the water?

V^2 = Vo + 2g*d

V^2 = 0 + 19.6*(12-6) = 117.6
V = 10.84 m/s.

V^2 = 0 + 19.6*12 = 235.2
V = 15.34 m/s

To calculate the speed of the diver at a certain point, we can use the principle of conservation of mechanical energy. The total mechanical energy of the system remains constant throughout the motion.

Let's denote the speed of the diver at a certain point as v and the height at that point as h.

1. Speed 6m above the water surface:
Initially, the diver has potential energy due to his height, which can be calculated using the equation: Potential energy = mass x gravity x height (PE = mgh). The gravitational potential energy gets converted into kinetic energy as the diver falls.

So, at a height of 6 m above the water surface, the potential energy will be Potential energy = m x g x 6.

To find the kinetic energy at this point, we can subtract the potential energy from the total mechanical energy of the system. The kinetic energy is given by the equation:
Kinetic energy = Total mechanical energy - Potential energy.

2. Speed just before striking the water:
At the water surface, the height of the diver is zero, so the potential energy is also zero. The entire potential energy has been converted to kinetic energy.

To find the kinetic energy just before the diver strikes the water, we can use the same equation as before: Kinetic energy = Total mechanical energy - Potential energy.

Once we have the kinetic energy, we can convert it to speed using the equation:
Kinetic energy = 1/2 x mass x velocity^2.

Now, let's calculate the speeds:

1. Speed 6m above the water surface:
Potential energy = m x g x 6
Kinetic energy = Total mechanical energy - Potential energy
Speed = sqrt((2 x Kinetic energy) / mass)

2. Speed just before striking the water:
Potential energy = 0
Kinetic energy = Total mechanical energy - Potential energy
Speed = sqrt((2 x Kinetic energy) / mass)

By applying these calculations, you will be able to find the speeds at both points. Just make sure to substitute the appropriate values for mass, height, and gravitational acceleration (g).