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=−4.9t^2+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 2 110 1 tenth 5

1 answer

To determine a reasonable scale for the range when setting up a table to find out when the rock hits the water, we first need to find the time at which the height \( h \) becomes 0 (when the rock hits the water). The given equation is:

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

We need to solve for \( t \) when \( h = 0 \):

\[ 0 = -4.9t^2 + 10 \] \[ 4.9t^2 = 10 \] \[ t^2 = \frac{10}{4.9} \] \[ t^2 \approx 2.04 \] \[ t \approx \sqrt{2.04} \approx 1.43 \text{ seconds} \]

Since the rock will hit the water after approximately 1.43 seconds, a reasonable range for the time scale in your table could be from 0 to about 2 seconds.

Among the response options provided (10, 2, 110, 1 tenth, 5), the best choice for the time range scale is 2, as it reasonably captures the time it takes for the rock to hit the water.