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

110
1 tenth

10
10

5
5

2

1 answer

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 that models the situation is:

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

Setting \( h \) to 0 gives us:

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

Rearranging the equation:

\[ 4.9t^2 = 10 \] \[ t^2 = \frac{10}{4.9} \] \[ t^2 \approx 2.0408 \] \[ t \approx \sqrt{2.0408} \approx 1.43 \text{ seconds} \]

Since the rock hits the water at approximately 1.43 seconds, a reasonable scale for the range (time in seconds) in a table would be one that captures this timing effectively.

Looking at the provided options:

  • 1tenth (which means using increments of 0.1 seconds) would allow for a very fine scale.
  • 2 seconds might also be reasonable since it covers the 1.43 seconds mark comfortably.

The best reasonable scale for the range would likely be 1 tenth (0.1 seconds), as it gives more detail around the time when the rock hits the water. However, 2 seconds would also work but may not provide as much granularity as the tenths.

Therefore, the most suitable choice from the provided options is: 1 tenth.