Final answer:
The known values include initial velocity, acceleration due to gravity, and final velocity at the peak of the jump. The dolphin rises 8.6 meters above the water, and the total air time is calculated to be approximately 2.65 seconds. These results are based on kinematic equations and the physical characteristics of dolphins.
Step-by-step explanation:
A student asks about the motion of a dolphin jumping out of the water. The questions involve using the known initial velocity and acceleration due to gravity to find how high the dolphin rises above the water and how long it stays in the air. To solve these queries, we need physics concepts and kinematic equations.
List of Knowns:
- Initial velocity (v_i) = 13.0 m/s
- Acceleration due to gravity (a) = -9.80 m/s² (negative indicates direction towards Earth)
- Final velocity (v_f) at the highest point = 0 m/s (the dolphin stops ascending)
Height Calculation:
To calculate the height (y), we use the kinematic equation:
y = v_i² / (2 * a)
Plugging the known values into the equation, we get:
y = (13.0 m/s)² / (2 * -9.80 m/s²) = 8.6 m
This height is reasonable, as dolphins can jump several times their body length out of the water.
Air Time Calculation:
To obtain the time (t) the dolphin is in the air, we use the equation:
t = 2 * (v_i / |a|)
And we find that:
t = 2 * (13.0 m/s) / 9.80 m/s² = 2.65 s