Final answer:
To determine how long the swimmer's feet are in the air, the kinematic equation of motion is used, which leads to a quadratic equation. By substituting the known values into the equation, we find that the swimmer's feet are in the air for approximately 1.02 seconds.
Step-by-step explanation:
To solve this physics problem, we need to calculate the total time the swimmer's feet are in the air due to gravity. The swimmer starts with a velocity of 4.00 m/s and is 1.80 m above the pool. We can use the kinematic equation for motion under constant acceleration (gravity, in this case).
The equation is s = ut + 1/2at², where:
- s is the displacement (1.80 m downwards in this case),
- u is the initial velocity (4.00 m/s upwards),
- a is the acceleration due to gravity (-9.8 m/s², the negative sign indicates the direction is opposite to the initial velocity),
- t is the time we are looking to find.
Rearranging the equation to solve for time, we get a quadratic equation in the form 0 = 1/2at² - ut - s. Substituting the known values, we have 0 = (1/2)(-9.8)t² - (4.00)t - (1.80). Using the quadratic formula, we get two possible times, but we only consider the positive time because time can't be negative in our scenario. This gives us the time her feet are in the air until she hits the water.
Using the quadratic formula, we find the time to be approximately 1.02 seconds.