Final answer:
To determine the time it took for the dolphin to reach the highest point of the jump, the kinematic equations were used with an estimated gravity acceleration of 10 m/s². By calculating the initial velocity and using it to find the time, we established that the dolphin took approximately 1.34 seconds to reach the apex of its jump.
Step-by-step explanation:
To find out how long it took the dolphin to reach the highest point of its 9-meter jump, we can use the kinematic equations for uniformly accelerated motion, assuming the acceleration due to gravity is 10 m/s2 and upward motion is positive. The relevant equation in this scenario is:
final velocity2 = initial velocity2 - 2 × gravity × height
At the highest point, the dolphin's final velocity is 0 m/s. Rearranging the formula and solving for the initial velocity:
0 m/s2 = initial velocity2 - 2 × 10 m/s2 × 9 m
From this, we find the initial velocity to be approximately 13.4 m/s. Using this initial velocity, we can determine the time to reach the highest point using the equation:
final velocity = initial velocity - gravity × time
Rearranging to solve for time we get:
time = (initial velocity - final velocity) / gravity
time = (13.4 m/s - 0 m/s) / 10 m/s2
time = 1.34 s
The dolphin took approximately 1.34 seconds to reach the highest point of its jump, which is a reasonable result considering dolphins can jump several times their body length out of the water.