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

1 answer

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

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

Setting \( h \) to 0, we can solve for \( t \):

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

Rearranging gives us:

\[ 4.9t^2 = 10 \]

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

\[ t^2 \approx 2.04 \]

Taking the square root:

\[ t \approx \sqrt{2.04} \]

\[ t \approx 1.43 , \text{seconds} \]

Since the rock hits the water after approximately 1.43 seconds, a reasonable scale for the range of time \( t \) can be from \( 0 \) to \( 2 \) seconds. The best option that fits this range would be:

2 seconds.

Thus, the answer is 2.