Final answer:
To find the diver's speed 5.00 m above the water surface using the conservation of mechanical energy, we can equate the initial gravitational potential energy at the top of the dive with the final kinetic energy at 5.00 m above the water surface. Substituting the known values, the speed is calculated to be 13.84 m/s.
Step-by-step explanation:
To find the diver's speed 5.00 m above the water surface using the conservation of mechanical energy, we can apply the principle of conservation of mechanical energy, which states that the total mechanical energy of a system remains constant as long as no external forces are acting on it. At 5.00 m above the water surface, the only form of mechanical energy the diver has is gravitational potential energy. Therefore, we can equate the initial gravitational potential energy at the top of the dive with the final kinetic energy at 5.00 m above the water surface.
Using the formula for gravitational potential energy: PE = mgh, where m is the mass of the diver, g is the acceleration due to gravity, and h is the height, we can calculate the initial potential energy at the top of the dive. Then, using the formula for kinetic energy: KE = 0.5mv^2, where m is the mass of the diver and v is the speed, we can solve for the speed at 5.00 m above the water surface.
Let's plug in the known values: m = 75.0 kg, g = 9.8 m/s^2, and h = 9.10 m. At the top of the dive, the potential energy is given by PE = mgh = 75.0 kg * 9.8 m/s^2 * 9.10 m. To find the speed at 5.00 m above the water surface, we equate this potential energy to the kinetic energy: KE = 0.5mv^2 = PE. Solving for v, we get v = sqrt(2gh).
Let's substitute the values and calculate the speed:
v = sqrt(2 * 9.8 m/s^2 * 9.10 m) = 13.84 m/s