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A student drops a ball from a height of 60 meters. The table below shows the ball’s speed and height as time passes.

5 answers

It seems like you’re referring to a table that includes data on the ball's speed and height over time, but the table itself isn't provided. However, I can help you understand how a ball behaves when dropped from a height and what the expected speed and height measurements might be like over time.

When an object is dropped from a height (neglecting air resistance), it will accelerate downwards due to gravity at approximately \(9.81 , m/s^2\). Here’s a typical breakdown of what happens when a ball is dropped from 60 meters:

  1. Initial Conditions:

    • Height = 60 meters
    • Initial speed = 0 m/s (since it is dropped)

  2. After 1 second:

    • Height can be calculated using the formula: \[ h = h_0 - \frac{1}{2} g t^2 \]
    • Where \(h_0\) is the initial height, \(g\) is the acceleration due to gravity, and \(t\) is time in seconds.
    • Speed can be calculated as: \[ v = g t \]

  3. Calculating at intervals:

    • You would calculate the height and speed at different intervals (e.g., every second) until it hits the ground (when height = 0).

Here is an example of how you might fill out such a table:

| Time (s) | Height (m) | Speed (m/s) | |----------|------------|--------------| | 0 | 60 | 0 | | 1 | 54.9 | 9.81 | | 2 | 39.2 | 19.62 | | 3 | 24.5 | 29.43 | | 4 | 9.8 | 39.24 | | 5 | 0 | 49.05 |

In this table, height decreases as time increases until it reaches 0 meters when the ball hits the ground, while speed increases due to gravitational acceleration.

If you have specific data points in mind or additional questions regarding the motion, please share them, and I can provide a more tailored explanation!

A. At the start (0 seconds)
B. After 0.5 seconds
C. After 2 seconds
D. After 2.5 seconds

To calculate the height and speed of a ball dropped from a height of 60 meters at the given times, we'll use the following equations of motion under constant acceleration due to gravity \( (g \approx 9.81 , m/s^2) \):

  1. Height Equation: \[ h = h_0 - \frac{1}{2} g t^2 \] where \( h_0 \) is the initial height (60 meters).

  2. Speed Equation: \[ v = g t \]

Calculations:

  1. At the Start (0 seconds):

    • Height: \[ h = 60 - \frac{1}{2} \cdot 9.81 \cdot 0^2 = 60 , m \]
    • Speed: \[ v = 9.81 \cdot 0 = 0 , m/s \]

  2. After 0.5 seconds:

    • Height: \[ h = 60 - \frac{1}{2} \cdot 9.81 \cdot (0.5)^2 \approx 60 - \frac{1}{2} \cdot 9.81 \cdot 0.25 \approx 60 - 1.22625 \approx 58.77 , m \]
    • Speed: \[ v = 9.81 \cdot 0.5 \approx 4.905 , m/s \]

  3. After 2 seconds:

    • Height: \[ h = 60 - \frac{1}{2} \cdot 9.81 \cdot (2)^2 \approx 60 - \frac{1}{2} \cdot 9.81 \cdot 4 \approx 60 - 19.62 \approx 40.38 , m \]
    • Speed: \[ v = 9.81 \cdot 2 \approx 19.62 , m/s \]

  4. After 2.5 seconds:

    • Height: \[ h = 60 - \frac{1}{2} \cdot 9.81 \cdot (2.5)^2 \approx 60 - \frac{1}{2} \cdot 9.81 \cdot 6.25 \approx 60 - 30.703125 \approx 29.30 , m \]
    • Speed: \[ v = 9.81 \cdot 2.5 \approx 24.525 , m/s \]

Summary of Results:

| Time (s) | Height (m) | Speed (m/s) | |----------|------------|--------------| | 0 | 60.00 | 0.00 | | 0.5 | 58.77 | 4.91 | | 2 | 40.38 | 19.62 | | 2.5 | 29.30 | 24.53 |

These calculations show the height and speed of the ball at each specified time. If you have further questions or need more calculations, feel free to ask!

which one
a
b
c
d?

Here's a summary of the results with specific labels:

A. At the Start (0 seconds):

  • Height: 60.00 meters
  • Speed: 0.00 m/s

B. After 0.5 seconds:

  • Height: 58.77 meters
  • Speed: 4.91 m/s

C. After 2 seconds:

  • Height: 40.38 meters
  • Speed: 19.62 m/s

D. After 2.5 seconds:

  • Height: 29.30 meters
  • Speed: 24.53 m/s

So, here are the values associated with each letter:

  • A: Height = 60.00 m, Speed = 0.00 m/s
  • B: Height = 58.77 m, Speed = 4.91 m/s
  • C: Height = 40.38 m, Speed = 19.62 m/s
  • D: Height = 29.30 m, Speed = 24.53 m/s

If you need to choose among these for a specific question or context, please let me know the context or the specific question!