Final answer:
The swimmer's feet are in the air for approximately 0.816 seconds. Her highest point above the board is approximately 1.62 meters. Her velocity when her feet hit the water is approximately -4.00 m/s.
Step-by-step explanation:
(a) How long are her feet in the air?
To find the time her feet are in the air, we need to calculate the time it takes for her to reach the highest point and then double it. The time taken to reach the highest point can be found using the equation:
vf = vi + at
Where vf is the final velocity (0 m/s at the highest point), vi is the initial velocity (4.00 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time taken. Rearranging the equation, we get:
t = (vf - vi) / a
t = (0 - 4.00) / -9.8
t ≈ 0.408 s
Therefore, the time her feet are in the air is approximately 2(0.408 s) = 0.816 s.
(b) What is her highest point above the board?
At the highest point, her velocity is 0 m/s. Using the equation:
vf = vi + at
We can find the time it takes for her to reach the highest point:
t = (vf - vi) / a
t = (0 - 4.00) / -9.8
t ≈ 0.408 s
Using the equation:
d = vi * t + 0.5 * a * t^2
We can find the height of the highest point:
d = 4.00 * 0.408 + 0.5 * (-9.8) * (0.408)^2
d ≈ 1.62 m
Therefore, her highest point above the board is approximately 1.62 m.
(c) What is her velocity when her feet hit the water?
When her feet hit the water, her final velocity can be found using the equation:
vf = vi + at
Where vf is the final velocity, vi is the initial velocity (0 m/s at the highest point), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time taken. Rearranging the equation, we get:
vf = vi + a * t
Substituting the known values, we have:
vf = 0 + (-9.8) * 0.408
vf ≈ -4.00 m/s
Therefore, her velocity when her feet hit the water is approximately -4.00 m/s.