Calculating the Diving Time of Diana: A Detailed Analysis

Diana, at a pool, dives from a diving board with an initial velocity of 7.6 m/s. She travels 8.42 meters until she comes to a complete stop. This article dives into the detailed process of calculating how long it took for Diana to stop, using kinematic equations and the principles of physics.

Using Kinematic Equations to Find Diana's Stopping Time

To calculate the time it took for Diana to come to a complete stop, we can use the kinematic equation that relates distance, initial velocity, final velocity, acceleration, and time:

d v_i t - frac{1}{2} a t^2

In this scenario:

d 8.42 m - the distance she traveled until she stopped. v_i 7.6 m/s - the initial velocity of Diana when she dove into the water. v_f 0 m/s - the final velocity since she came to a complete stop.

The acceleration (a) is negative as it is a deceleration (slowing down). We can use the kinematic equation for final velocity to find the acceleration:

v_f^2 v_i^2 - 2a d

Substituting the known values:

0 7.6^2 - 2a(8.42)

Calculating (7.6^2):

57.76 -2a(8.42)

Solving for a:

a -frac{57.76}{16.84} approx -3.43 , text{m/s}^2

Now we can use the first kinematic equation to find the time (t):

v_f v_i a t

Substituting the known values:

0 7.6 - 3.43t

Solving for t:

3.43t 7.6

t frac{7.6}{3.43} approx 2.21 text{ seconds}

Therefore, the time it took for Diana to come to a stop is approximately 2.21 seconds.

Implications of the Diving Scenario

It's important to note that Diana will not stop immediately upon hitting the water surface. Due to the impulse given to her by the water, she will continue to move downward for some time. The provided information, such as the depth of the pool and Diana's mass, is crucial for a more accurate calculation. Without these details, we cannot solve for the stopping time accurately.

The depth of the pool and the mass of Diana would provide more precise values for the deceleration (a) and could potentially change the stopping time. Nonetheless, the simplified analysis based on the given information still offers a reasonable estimate of the time taken for Diana to stop.

Conclusion

In conclusion, utilizing the principles of physics and kinematic equations, we can effectively analyze Diana's diving scenario to calculate the time it took for her to stop. The key is understanding the relationship between velocity, acceleration, and time in the context of her dive.

For a more accurate analysis, consider gathering additional data such as the pool depth and Diana's mass to fine-tune the calculations.