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

10
10

2
2

5
5

110

Answer 1

To determine when the rock hits the water, we need to find the time \( t \) when the height \( h \) becomes 0 (i.e., when the rock reaches the lake).

The equation given is:

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

Setting \( h = 0 \) (when the rock hits the water):

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

Solving for \( t \):

\[
4.9t^2 = 10
\]

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

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

Since \( t \) is approximately 1.43 seconds, a reasonable scale for the range would be from 0 to around 2 seconds.

Given the options, here are the possible ranges:
- 10 seconds (too large)
- 2 seconds (reasonable)
- 5 seconds (too large)
- 110 seconds (much too large)

Therefore, the most appropriate choice for the scale of the range is **2 seconds**.