Question

Quadratic Functions from Situations Quick Check
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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

10
10

5
5

110
1 tenth
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Answer 1

To determine when the rock hits the water, we need to find when the height \( h \) is equal to 0 (when it reaches the lake). The equation given is:

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

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

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

This can be rearranged to find \( t \):

\[ 4.9t^2 = 10 \]

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

\[ t^2 \approx 2.04 \]

Taking the square root of both sides:

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

Now, when setting up a table to determine when the rock hits the water, we should consider a reasonable time scale for \( t \), such as increments of seconds leading up to about 1.5 seconds.

Looking at the provided response options for the range:

- 2
- 10
- 5
- 110
- 1 tenth

A reasonable scale for the range would be **2**, as it allows you to set up a table with entries like \( 0, 1, 2 \), which comfortably includes the time it takes for the rock to hit the water (approximately 1.43 seconds).