Final answer:
Gravity doesn't stop a dolphin from leaving the water because the dolphin generates enough hydrodynamic lift by pushing against the water to overcome the force of gravity temporarily. The roles of buoyancy and kinematic principles apply when calculating the height of the jump and the time spent airborne.
Step-by-step explanation:
The reason gravity doesn't stop the dolphin from leaving the water when it leaps is due to the hydrodynamic lift. When a dolphin jumps, it uses its muscles to exert a force on the water, which in turn exerts an equal and opposite force on the dolphin, propelling it upward. This action is in accordance with Newton's third law of motion. While gravity does act on the dolphin, pulling it back towards the water, the initial velocity the dolphin achieves by pushing against the water allows it to overcome the force of gravity momentarily and leap out of the water.
Buoyancy also plays a role, as it creates an upward force on any object submerged in a fluid, but it's primarily the hydrodynamic lift that allows the dolphin to lift off and clear the water. When a dolphin jumps out of the water at a velocity of 13.0 m/s, we can use kinematic equations to calculate the maximum height it reaches and the time it spends in the air. The knowns in this problem are the initial velocity (13.0 m/s), the acceleration due to gravity (-9.81 m/s2), and the final velocity (0 m/s at the peak of its jump). Using these values, we can solve for the height and the time the dolphin is in the air.