An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by h(t) = -16t2 + 80t + 200.
That is correct.
To find the maximum height reached by the object, we need to determine the vertex of the parabolic function h(t) = -16t^2 + 80t + 200.
The vertex of a parabola can be found using the formula t = -b / (2a), where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.
In this case, a = -16 and b = 80. Substituting these values into the formula, we have:
t = -80 / (2 * -16) = -80 / -32 = 2.5
Therefore, the object reaches its maximum height after 2.5 seconds.
To calculate the maximum height, we substitute t = 2.5 into h(t):
h(2.5) = -16 * (2.5)^2 + 80 * 2.5 + 200
= -16 * 6.25 + 200 + 200
= -100 + 200 + 200
= 300 feet
Hence, the maximum height reached by the object is 300 feet.