Final answer:
The time it takes for the projectile to reach its maximum height is calculated using the vertex formula t=-b/(2a). For the given function s(t)=-16t²+8t, the projectile will reach its maximum height after 0.25 seconds.
Step-by-step explanation:
The question asks to find the time it takes for a projectile to reach its maximum height with a given height function s(t) = -16t² + 8t. This height function is a quadratic equation where the coefficient of t² is negative, indicating that the projectile will eventually reach a maximum height before descending back to the ground. The maximum height of the projectile occurs at the vertex of the parabola represented by this function.
To find the time at which the projectile reaches its maximum height, we can use the formula t = -b/(2a) where a is the coefficient of t² and b is the coefficient of t. In this case, a = -16 and b = 8. Plugging these values into the formula, we get t = -8/(2 × (-16)), which simplifies to t = 0.25 seconds.
Therefore, it will take the projectile 0.25 seconds to reach its maximum height.