Question

The height, h(t), in feet, of a projectile launched from a 26-foot tall tower is modeled by the equation h(t) = −16t^2 + 64t + 26, where t represents the time after launch, in seconds. What is the maximum height, in feet, reached by the projectile?

a) 64 feet
b) 90 feet
c) 104 feet
d) 128 feet

Answer 1

The maximum height reached by the projectile is 104 feet.

Step-by-step explanation:

The maximum height reached by the projectile can be determined by finding the vertex of the quadratic equation that models the projectile's height. In this case, the equation is h(t) = -16t^2 + 64t + 26. The maximum height is achieved at the vertex of the parabola, which corresponds to the t-value that makes the coefficient of the t^2 term zero.

To find this t-value, we can use the formula t = -b/2a, where a, b, and c are the coefficients of the equation. In this case, a = -16 and b = 64, so the t-value is t = -64/(2*(-16)) = 2 seconds.

Substituting this t-value back into the equation, we get h(2) = -16*(2)^2 + 64*(2) + 26 = 104 feet. Therefore, the maximum height reached by the projectile is 104 feet.