Question

A rock is dropped from a bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation below.



`h\left(t\right)=-16t^{2}+320`

How long will it take the rock to reach the river?

Answer 1

To find the time it takes for the rock to reach the river, we need to set the height function `h(t)` equal to 0 and solve for `t`:

`-16t^2 + 320 = 0`

Add 16t^2 to both sides:

320 = 16t^2

Divide by 16:

t^2 = 20

Take the square root of both sides to solve for t:

t = sqrt(20) ≈ 4.47 seconds

So, it will take approximately 4.47 seconds for the rock to reach the river.