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
ℎ
=
−
4.9
𝑡
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

5
5

2
2

110
1
10
1 tenth

10
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, which can be found by setting the equation:

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

Solving for \( t \):

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

\[ 4.9t^2 = 10 \]

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

\[ t^2 \approx 2.0408 \]

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

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

To set up a table to determine when the rock hits the water, the reasonable scale for the range would be from \( t = 0 \) seconds to \( t \approx 1.5 \) seconds.

Considering the given responses, the scales that would make sense would allow for decimal increments, so:

- **1 tenth (1, 1.1, 1.2, ..., 1.5)** would be reasonable.

Therefore, the best choice for the range scale would be **1 tenth**.