The height of a missile (h), in feet, is given by the equation h=8000t-16t^2, where t us time in seconds. What is the time it takes to reach the maximum height?
0 = 8000t -16t^2
-16t( t-500) = 0
t = 0, t= 500
0r
Max = 500/2 = 250
Max
t = -b/2a
t = -8000/2(-16)
t = 250
To find the time it takes for the missile to reach its maximum height, we need to determine the vertex of the parabolic equation given. The vertex represents the maximum point of the parabola.
The equation of the missile's height is h = 8000t - 16t^2. This is in the form of h = at^2 + bt + c, where a, b, and c are constants. In this case, a = -16, b = 8000, and c = 0.
The x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by the formula x = -b / (2a). In our case, x represents time, so we'll substitute t for x in the formula.
Substituting the values into the formula:
t = -8000 / (2*(-16))
t = -8000 / (-32)
t = 250
Therefore, it takes 250 seconds for the missile to reach its maximum height.