The height `h`, in meters, of a launched projectile `t` seconds after it is launched is modeled by the function `h(t) =…

The question asks for the time `t` when the height `h(t)` is 40 meters for the first time. The function for the projectile's height is `h(t) = -5t² + 20t + 25`. To find the time when the height is 40 meters, set `h(t)` equal to 40:

`40 = -5t² + 20t + 25`

Subtract 40 from both sides to set the equation to zero:

`0 = -5t² + 20t - 15`

To simplify, divide the entire equation by -5:

`0 = t² - 4t + 3`

Factor the quadratic expression:

`0 = (t - 1)(t - 3)`

This equation has two solutions for `t`: `t = 1` and `t = 3`. Both are times when the projectile is at a height of 40 meters (on its way up and on its way down). The question asks for the · first · time this occurs, which is the smaller of the two values.

Therefore, the correct answer is `t = 1`.

Choice B is incorrect because `t=2` is the time when the projectile reaches its maximum height, not a height of 40 meters.

Choice C is incorrect because `t=3` is the second time the projectile reaches a height of 40 meters, not the first time.

Choice D is incorrect because `t=5` is a time when the projectile's height would be 0 meters (if we solve `h(t)=0`), not 40 meters.