Final answer:
The dolphin reaches a height of approximately 9.32 meters above the water.
Step-by-step explanation:
To solve this problem, we can use the equation for projectile motion. Let's first list the knowns: initial velocity (13.0 m/s), final velocity (0 m/s), and acceleration (-9.80 m/s²). The unknown in this problem is the height the dolphin reaches above the water. To find this, we can use the equation: final velocity squared = initial velocity squared + 2 * acceleration * displacement. Rearranging the equation to solve for displacement, the height the dolphin reaches, we get: displacement = (final velocity squared - initial velocity squared) / (2 * acceleration). Plugging in the known values, we can calculate the displacement as follows: displacement = (0 m/s)^2 - (13.0 m/s)^2 / (2 * -9.80 m/s²). Solving this equation, we find that the dolphin reaches a height of approximately 9.32 meters above the water.