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

5
5

2
2

10
10

110
1 tenth

Answer 1

To determine when the rock hits the water, we need to find when the height \( h \) is 0 (i.e., when the rock reaches the surface of the lake). Thus, we can set up the equation:

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

This simplifies to:

\[
4.9t^2 = 10
\]
\[
t^2 = \frac{10}{4.9}
\]
\[
t^2 \approx 2.04
\]
\[
t \approx \sqrt{2.04} \approx 1.43 \text{ seconds}
\]

Since the time until the rock hits the water is approximately 1.43 seconds, we can set up a table for \( t \) with reasonable increments.

Given these options:

- 5
- 2
- 10
- 110
- 1 tenth

A reasonable scale for the range, considering the time until impact is around 1.43 seconds, would be **2** seconds. This allows for a manageable table that covers from 0 to at least 2 seconds.