Final answer:
The equation provided represents the height of a projectile launched into the air as a function of time. The time it takes for the projectile to reach its maximum height can be found using the equation for the vertex of a parabola.4 seconds.
Step-by-step explanation:
In projectile motion, an object is launched into the air and follows a curved path due to the influence of gravity. The equation provided, s = -16t²+128t, represents the height of the projectile as a function of time, with 's' being the height above ground and 't' being the time elapsed since launch.
To find the time it takes for the projectile to reach its maximum height, we can use the equation for the vertex of a parabola: t = -b/2a. In this case, a = -16 and b = 128. Plugging these values into the equation gives us t = -128/(-32) = 4 seconds.
Therefore, the projectile takes 4 seconds to reach its maximum height.