The problem describes a plane making a loop in the air, with its height modeled by the function $h(t) = 300\cos(\frac{\pi}{16}t) + 800$, where $h$ is in meters and $t$ is in seconds. We need to find the height of the plane after 8 seconds.

1. Problem Description

The problem describes a plane making a loop in the air, with its height modeled by the function $h(t) = 300\cos(\frac{\pi}{16}t) + 800$, where $h$ is in meters and $t$ is in seconds. We need to find the height of the plane after 8 seconds.

2. Solution Steps

We are given the function $h(t) = 300\cos(\frac{\pi}{16}t) + 800$. We need to find the value of $h(8)$.

Substitute $t = 8$ into the function:

$h(8) = 300\cos(\frac{\pi}{16}(8)) + 800$

$h(8) = 300\cos(\frac{\pi}{2}) + 800$

Since $\cos(\frac{\pi}{2}) = 0$, we have:

$h(8) = 300(0) + 800$

$h(8) = 0 + 800$

$h(8) = 800$

3. Final Answer

The height of the plane after 8 seconds is 800 meters.