Final answer:
To determine the mechanical energy of the diver, calculate the gravitational potential energy at the initial height. The diver's speed at various points can be found using the conservation of mechanical energy, subtracting potential energy from total mechanical energy to get kinetic energy and then solving for speed.
Step-by-step explanation:
The question involves the principles of mechanics in physics, specifically dealing with mechanical energy, gravitational potential energy, kinetic energy, and the conservation of energy principle. When the diver initially drops from the board, the mechanical energy of the system is equal to their gravitational potential energy because their initial speed is zero.
The mechanical energy of the diver can be found using the equation for gravitational potential energy (PE), which is PE = mgh, where m is the mass of the diver, g is the acceleration due to gravity, and h is the height above the water surface. With a known force (weight) of the diver, we can find their mass by dividing the force by the acceleration due to gravity (m = F/g). Then, mechanical energy is equal to mgh at the height of 10.0 m.
To find the diver's speed 5.00 m above the water's surface, we first need to calculate the potential energy at that height and then use the conservation of mechanical energy to find the kinetic energy at that point, since the total mechanical energy remains constant. The kinetic energy (KE) at 5.00 m can be found by subtracting the potential energy at this height from the total mechanical energy. The diver's speed (v) can then be calculated using the equation for kinetic energy (KE = 0.5mv^2), solving for v.
Similarly, the diver's speed just before striking the water can be found by considering that all potential energy has been converted into kinetic energy at the point of impact with the water because the height is 0 m. Using the total mechanical energy which equals the initial potential energy at 10.0 m, we again use the kinetic energy equation to solve for the diver's speed at impact.