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

110
1 tenth

2
2

5

Answer 1

To determine when the rock hits the water, we need to find the time \( t \) when the height \( h \) becomes 0 (since the rock will be at water level at that point).

The height equation provided is:
\[ h = -4.9t^2 + 10 \]

Setting \( h \) to 0 to find when the rock hits the water:
\[ 0 = -4.9t^2 + 10 \]
\[ 4.9t^2 = 10 \]
\[ t^2 = \frac{10}{4.9} \]
\[ t^2 \approx 2.0408 \]
\[ t \approx \sqrt{2.0408} \]
\[ t \approx 1.43 \text{ seconds} \]

Since we want to set up a table to determine when the rock hits the water, we need to choose a reasonable range for \( t \). Given that the rock hits the water around 1.43 seconds, a reasonable scale for the range would be from 0 to about 2 seconds, which allows us to capture the entire interval.

Among the options provided:

- **10**: too large a scale (0-10 seconds)
- **110**: way too large
- **2**: if interpreted as 0 to 2 seconds, this could work
- **5**: also large but if interpreted as 0-5 seconds could work

Based on this analysis, **2** is the most reasonable scale, as it limits the time frame effectively to capture when the rock hits the water.