Final answer:
The diver's highest point above the board is 0.816 m. Her feet are in the air for 0.408 seconds. Her velocity when her feet hit the water is approximately 0.0016 m/s.
Step-by-step explanation:
To find the highest point above the diving board, we need to determine the maximum height reached by the diver. From the given information, we know that the initial velocity of the diver is 4.00 m/s and the takeoff point is 1.80 m above the pool. We can use the kinematic equation for vertical motion in the absence of air resistance to calculate the maximum height:
Final Velocity^2 = Initial Velocity^2 + 2 * acceleration * displacement
At the highest point, the final velocity will be 0 m/s, so we can write the equation as:
0 = (4.00 m/s)^2 + 2 * (-9.8 m/s^2) * displacement
Solving for the displacement, we find:
displacement = (4.00 m/s)^2 / (2 * 9.8 m/s^2) = 0.816 m
Therefore, the diver's highest point above the board is 0.816 m.
To determine the time her feet are in the air, we can use the equation:
Final Velocity = Initial Velocity + acceleration * time
Since the final velocity when her feet hit the water is 0 m/s, we can write the equation as:
0 = 4.00 m/s + (-9.8 m/s^2) * time
Solving for time, we find:
time = -4.00 m/s / (-9.8 m/s^2) = 0.408 s
Therefore, her feet are in the air for 0.408 seconds.
Finally, to determine her velocity when her feet hit the water, we can use the equation:
Final Velocity = Initial Velocity + acceleration * time
Since the initial velocity when she starts bouncing is 4.00 m/s, we can write the equation as:
Final Velocity = 4.00 m/s + (-9.8 m/s^2) * 0.408 s
Solving for the final velocity, we find:
Final Velocity = 4.00 m/s + (-3.9984 m/s) = 0.0016 m/s
Therefore, her velocity when her feet hit the water is approximately 0.0016 m/s.