Final answer:
To find the maximum height of a projectile given the equation h=−16t²+184t, calculate the vertex of the parabola using t = -b/(2a) to find the time at peak height, and then substitute that value back into the equation to determine the maximum height, which is 529 feet.
Step-by-step explanation:
To find the maximum height of a projectile using the given quadratic equation h=−16t²+184t, we can use the vertex form of a parabola. Since the coefficient of the t² term is negative, the parabola opens downward, and the vertex represents the maximum point. In this case, the vertex can be found using the formula t = -b/(2a), where a is the coefficient of the t² term, and b is the coefficient of the t term in the quadratic equation.
By substituting the coefficients a = -16 and b = 184 into the formula, we evaluate the time t at which the projectile reaches its maximum height: t = -184/(2 × -16) = 5.75 seconds. To find the maximum height, we substitute this time back into the original equation: h = -16(5.75)² + 184(5.75), which yields the maximum height.
After simplifying the calculations, we find that the maximum height of the projectile is 529 feet.