or each value below, enter the number correct to four decimal places.

Suppose an arrow is shot upward on the moon with a velocity of 26 m/s, then its height in meters after t  seconds is given by  h(t)=26t-0.83t^2.
. Find the average velocity over the given time intervals.

[4, 5]:   
  

[4, 4.5]:   
  

[4, 4.1]:   
  

[4, 4.01]:   
  

[4, 4.001]:   

To calculate the average velocity of the arrow over the given time intervals, we use the formula for average velocity:

\[
\text{Average velocity} = \frac{h(t_2) - h(t_1)}{t_2 - t_1}
\]

Where \( h(t) = 26t - 0.83t^2 \), and \( t_1 \) and \( t_2 \) are the times at the start and end of the interval.

### Time interval [4, 5]
\[
\text{Average velocity} = \frac{h(5) - h(4)}{5 - 4}
\]

### Time interval [4, 4.5]
\[
\text{Average velocity} = \frac{h(4.5) - h(4)}{4.5 - 4}
\]

### Time interval [4, 4.1]
\[
\text{Average velocity} = \frac{h(4.1) - h(4)}{4.1 - 4}
\]

### Time interval [4, 4.01]
\[
\text{Average velocity} = \frac{h(4.01) - h(4)}{4.01 - 4}
\]

### Time interval [4, 4.001]
\[
\text{Average velocity} = \frac{h(4.001) - h(4)}{4.001 - 4}
\]

Let's calculate each one step by step.Here are the average velocities over each time interval, rounded to four decimal places:

1. **For [4, 5]:** 18.5300 m/s
2. **For [4, 4.5]:** 18.9450 m/s
3. **For [4, 4.1]:** 19.2770 m/s
4. **For [4, 4.01]:** 19.3517 m/s
5. **For [4, 4.001]:** 19.3592 m/s

Would you like further details or clarification on any step?

Here are 5 related questions to deepen your understanding:
1. What does the average velocity represent in this context?
2. How would you calculate the instantaneous velocity at \( t = 4 \)?
3. What is the significance of smaller time intervals in finding average velocity?
4. How would the results differ if the arrow were shot on Earth instead of the Moon?
5. Can you determine when the arrow reaches its maximum height?

**Tip:** As the time interval decreases, the average velocity approaches the instantaneous velocity at a specific point.

Suppose an arrow is shot upward on the moon with a velocity of 26 m/s, then its height in meters after t seconds is given by h(t)=26t-0.83t^2. Find the average velocity over the given time intervals.

Learn how to calculate the average velocity of an arrow shot upwards on the moon. This problem involves using the formula for average velocity and the quadratic function for height. The solution covers intervals [4, 5], [4, 4.5], [4, 4.1], [4, 4.01], and [4, 4.001], with answers rounded to four decimal places.

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