3. at an amusement park, a swimmer uses a water slide to enter the main pool. if the swimmer starts at rest…

3. at an amusement park, a swimmer uses a water slide to enter the main pool. if the swimmer starts at rest, slides without friction, and descends through a vertical height of $2.31\\text{ m}$, what is her speed at the bottom of the slide?

3. at an amusement park, a swimmer uses a water slide to enter the main pool. if the swimmer starts at rest, slides without friction, and descends through a vertical height of $2.31\\text{ m}$, what is her speed at the bottom of the slide?

Answer

Explanation:

Step1: Identify the conservation of energy principle

$$mgh = \frac{1}{2}mv^2$$

Step2: Simplify the equation to solve for speed

$$v = \sqrt{2gh}$$

Step3: Substitute the known values into the equation

$$v = \sqrt{2 \cdot 9.81 , \text{m/s}^2 \cdot 2.31 , \text{m}}$$

Step4: Calculate the final velocity

$$v \approx 6.73 , \text{m/s}$$

Answer:

6.73 m/s