A rock is droop from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation h(t)=-16t^2+320. Approximately how long will it take the rock to reach the river

Question

2.5 seconds
3.5 seconds
3.8 seconds
4.5 seconds

Answer 1

To determine how long it takes for the rock to reach the river, we need to find the value of \( t \) when the height \( h(t) \) of the rock is 0 (i.e., when it reaches the river). The equation given is:

\[ h(t) = -16t^2 + 320 \]

To find when the rock hits the river, we set \( h(t) \) to 0:

\[ 0 = -16t^2 + 320 \]

Now, let's solve for \( t \):

1. Rearrange the equation: \[ 16t^2 = 320 \]

2. Divide both sides by 16: \[ t^2 = \frac{320}{16} = 20 \]

3. Take the square root of both sides: \[ t = \sqrt{20} \approx 4.47 \text{ seconds} \]

Therefore, the rock will take approximately 4.5 seconds to reach the river.