Question

While hiking, Marek throws a rock off a cliff that is roughly 10 meters above a lake. This situation is modeled by the equation h=−4.9t2+10 , with h representing the height in meters and t the time in seconds. If you were to set up a table to determine when the rock hits the water, what would be a reasonable scale for the range?(1 point) Responses

Answer 1

To determine when the rock hits the water using the given equation \( h = -4.9t^2 + 10 \), we need to find when the height \( h \) is equal to 0 (the height of the water).

Setting the equation to 0 gives:

\[
0 = -4.9t^2 + 10
\]

Solving for \( t \):

1. Rearranging the equation:
\[
4.9t^2 = 10
\]

2. Divide both sides by 4.9:
\[
t^2 = \frac{10}{4.9} \approx 2.04
\]

3. Now take the square root of both sides:
\[
t \approx \sqrt{2.04} \approx 1.43 \text{ seconds}
\]

To create a table, you want a reasonable scale for the range of time \( t \), which will help you see the rock's height at various times.

Since the rock hits the water at about \( t = 1.43 \) seconds, a reasonable scale for the time (t) might range from 0 to about 2 seconds, collecting values that might include increments of 0.1 seconds. This would look like:

| Time (t) | Height (h) |
|----------|------------|
| 0.0 | 10 |
| 0.1 | 9.95 |
| 0.2 | 9.80 |
| 0.3 | 9.19 |
| 0.4 | 8.16 |
| 0.5 | 6.75 |
| 0.6 | 4.96 |
| 0.7 | 2.79 |
| 0.8 | 0.24 |
| 0.9 | -2.79 |
| 1.0 | -5.76 |
| 1.5 | -14.63 |

In conclusion, a reasonable scale for the range of time for the table would be **0 to 2 seconds** with increments of **0.1 seconds**.