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=−4.9t^2+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 the time \( t \) when the height \( h \) is equal to 0 (i.e., when the rock reaches the lake). The equation given is:

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

Setting \( h \) to 0, we get:

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

Solving for \( t \):

\[
4.9t^2 = 10
\]

\[
t^2 = \frac{10}{4.9} \approx 2.0408
\]

\[
t \approx \sqrt{2.0408} \approx 1.43
\]

Now that we've determined that the rock will hit the water at approximately \( t = 1.43 \) seconds, a reasonable scale for the range of the table to show this would be around the time intervals surrounding 1.43 seconds.

Considering typical time interval choices, a scale of 0.5 seconds or 1 second would be practical. Since the options provided include whole numbers like 2, 5, and the precise scale of 1 tenth is not reasonably practical, the appropriate answer would be **2** seconds, ensuring you capture the relevant time leading up to when the rock hits the water.

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