Question

The height, h(t), in feet, of a projectile launched from a 26-foot tall tower is modeled by the equation h(t)=−16t²+64t+26, where t represents the time after launch, in seconds. What is the maximum height, in feet, reached by the projectile? Enter a numeric value in the sentence below.

The projectile reaches a maximum height of _____ feet.

Answer 1

The projectile reaches a maximum height of 66 feet.

Step-by-step explanation:

The maximum height reached by the projectile can be determined by finding the vertex of the quadratic equation h(t) = -16t² + 64t + 26.

The vertex of a quadratic equation in the form of y = ax² + bx + c is given by the x-coordinate x = -b/2a. In this case, a = -16 and b = 64. Plugging these values into the formula, we have x = -64/(2*(-16)) = 2.

The maximum height is given by h(2) = -16(2)² + 64(2) + 26 = 66 feet. Therefore, the projectile reaches a maximum height of 66 feet.