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

5
5

2
2

110
1 tenth

10

Answer 1

To determine when the rock hits the water using the equation \( h = -4.9t^2 + 10 \), we need to find the time \( t \) when the height \( h \) becomes 0 (the height of the water).

Setting the equation to 0:

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

Rearranging gives:

\[
4.9t^2 = 10
\]

Dividing both sides by 4.9:

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

Taking the square root:

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

Based on this calculation, the rock will hit the water approximately 1.43 seconds after it is thrown.

When setting up a table to represent this scenario, you should have a range that covers at least from \( t = 0 \) to \( t = 2 \) seconds to capture the moment when the rock hits the water.

Therefore, a reasonable scale for the range could be:

**2**

This choice allows you to see the time intervals leading up to when the rock contacts the water.