To determine how long it will take for the rock to reach the river, we need to set \( h = 0 \) in the equation \( h = -16t^2 + 130 \) and solve for \( t \).
The equation given is:
\[ h = -16t^2 + 130 \]
Setting \( h = 0 \):
\[ 0 = -16t^2 + 130 \]
Rearranging gives:
\[ 16t^2 = 130 \]
Dividing both sides by 16:
\[ t^2 = \frac{130}{16} = 8.125 \]
Taking the square root of both sides:
\[ t = \sqrt{8.125} \approx 2.85 \]
Since 2.85 seconds isn't one of the options given, let's check the options we have:
- 2.5 seconds
- 3.5 seconds
- 3.8 seconds
- 4.5 seconds
2.85 seconds is closer to 3.5 seconds than the others, which suggests that the rock would reach the river slightly after 2.5 seconds, but definitely before 4.5 seconds.
Hence, based on the options, the closest and most reasonable estimate is 3.5 seconds.
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