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

2
2

110
1 tenth

5
5

10

Answer 1

To determine when the rock hits the water, we need to find out when the height \( h \) becomes zero in the given equation \( h = -4.9t^2 + 10 \).

We can set up the equation to find when \( h = 0 \):

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

Rearranging this gives:

\[
4.9t^2 = 10
\]

\[
t^2 = \frac{10}{4.9} \approx 2.04
\]

\[
t \approx \sqrt{2.04} \approx 1.43 \text{ seconds}
\]

Since we’re interested in creating a table to determine when the rock hits the water, we want to include a reasonable range of time values that includes \( t \approx 1.43 \) seconds.

A reasonable scale for the range of time would be from 0 to a little over 1.5 seconds. Therefore, a scale interval of 0.5 seconds (0, 0.5, 1.0, 1.5 seconds) would be appropriate.

However, from the options you provided:

- **2**
- **10**
- **5**
- **1 tenth**

The most reasonable choice that would relate to the timing before the rock hits the water would be **2** seconds. This allows enough granularity around the estimated time of impact.

So, the answer is **2 seconds**.