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Generate random numbers to fill in the table and calculate. I’m a female and 155 cm so how high estimate I can jump and time

To help you estimate your vertical jump height and hang time, we'll use random numbers for the hang time and perform the calculations based on your information (female, 155 cm).

### Step 1: Generate random times for jumping and landing.
We will simulate three trials for the jumping and landing times.

Let’s generate random times for three trials:

- **Trial 1**: \( t_0 = 0.5 \, \text{seconds}, t_1 = 1.2 \, \text{seconds} \)
- **Trial 2**: \( t_0 = 0.6 \, \text{seconds}, t_1 = 1.4 \, \text{seconds} \)
- **Trial 3**: \( t_0 = 0.55 \, \text{seconds}, t_1 = 1.25 \, \text{seconds} \)

Using these, the hang time \( \Delta t = t_1 - t_0 \):

- **Trial 1**: \( \Delta t = 1.2 - 0.5 = 0.7 \, \text{seconds} \)
- **Trial 2**: \( \Delta t = 1.4 - 0.6 = 0.8 \, \text{seconds} \)
- **Trial 3**: \( \Delta t = 1.25 - 0.55 = 0.7 \, \text{seconds} \)

### Step 2: Calculate the average hang time.
\[
\text{Average Hang Time} = \frac{0.7 + 0.8 + 0.7}{3} = 0.733 \, \text{seconds}
\]

### Step 3: Calculate vertical jump height using the downward portion of motion.

We are given:
- \( a = -9.8 \, \text{m/s}^2 \)
- Initial velocity \( v_0 = 0 \, \text{m/s} \) at the top of the jump
- Hang time divided by 2 represents the time for the downward motion: \( t = \frac{\text{hang time}}{2} = \frac{0.733}{2} = 0.3665 \, \text{seconds} \)

Using the kinematic equation:
\[
y = v_0 t + \frac{1}{2} a t^2
\]
Since \( v_0 = 0 \):
\[
y = \frac{1}{2} (-9.8) (0.3665)^2 = \frac{1}{2} \times (-9.8) \times 0.1343 = -0.658 \, \text{m} \approx 0.658 \, \text{m}
\]
So, the estimated vertical jump height is **0.658 meters (65.8 cm)**.

### Step 4: Determine rating.
Using the chart in your image, for females, a vertical jump of 65.8 cm falls into the **"Excellent"** category (greater than 60 cm).

### Step 5: Calculate initial velocity (Step 5 on your sheet).
For this, we use the upward part of the motion and the kinematic equation:
\[
v_f = v_0 + at
\]
Here, \( v_f = 0 \, \text{m/s} \) at the top of the jump, \( a = -9.8 \, \text{m/s}^2 \), and \( t = 0.3665 \, \text{seconds} \):
\[
0 = v_0 + (-9.8)(0.3665)
\]
\[
v_0 = 9.8 \times 0.3665 = 3.59 \, \text{m/s}
\]
So, the initial velocity is **3.59 m/s**.

### Summary:
- **Vertical Jump Height**: 65.8 cm (Excellent category)
- **Initial Velocity**: 3.59 m/s

Would you like more details on any of these steps or have further questions?

### 5 Related Questions:
1. How does hang time affect vertical jump height?
2. What other factors can influence initial velocity during a jump?
3. How would the calculations change if the acceleration due to gravity was different (e.g., on the moon)?
4. How can improving leg strength affect both initial velocity and jump height?
5. What other sports benefit from vertical jump analysis?

### Tip:
Improving your squat strength can significantly enhance your vertical jump as it directly impacts your ability to generate explosive power in your legs.

Generate random numbers to fill in the table and calculate. I’m a female and 155 cm so how high estimate I can jump and time.

Learn how to estimate vertical jump height and calculate hang time using kinematic equations. This example includes detailed steps, simulated trials, and calculations based on the participant's height (155 cm). Formulas for free fall motion and velocity determination are applied, with results categorized using a rating chart.

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