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

110
1 tenth

10

Answer 1

To determine when the rock hits the water, we need to find the time \( t \) when the height \( h \) becomes 0. The equation given is:

\[
h = -4.9t^2 + 10.
\]

To find when the rock hits the water, we set \( h \) to 0:

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

Rearranging this gives:

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

Taking the square root of both sides gives:

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

Since the rock hits the water in approximately 1.43 seconds, a reasonable scale for the range of time (t) in a table would be from 0 to around 2 seconds. Given the options provided, each representing a different scale increment, a scale of **1** (such as 0, 1, 2) would be reasonable.

Thus, the best response among the provided options is **1**.