height of soccer ball is h(t)=-4.9t2+16t+0.5 what is maximum height of the ball reaches
To find the maximum height reached by the soccer ball, we need to determine the vertex of the quadratic function representing its height.
The quadratic function that describes the height of the soccer ball can be expressed as h(t) = -4.9t^2 + 16t + 0.5, where t represents time and h(t) represents height.
The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b / (2a).
In this case, the equation is h(t) = -4.9t^2 + 16t + 0.5, and we need to find the value of t that corresponds to the maximum height. Comparing it to the standard form of a quadratic equation, we have a = -4.9, b = 16, and c = 0.5.
Plugging these values into the formula, we can find the time (t) at which the ball reaches its maximum height:
t = -16 / (2*(-4.9))
t = -16 / (-9.8)
t ≈ 1.63 seconds
Therefore, the ball reaches its maximum height after approximately 1.63 seconds.
To find the maximum height (h), we substitute this time (t) back into the original function:
h(t) = -4.9t^2 + 16t + 0.5
h(1.63) = -4.9(1.63)^2 + 16(1.63) + 0.5
h(1.63) ≈ 13.1 meters
Therefore, the maximum height reached by the ball is approximately 13.1 meters.
Re-wording your problem:
find the vertex of the parabola h = -4.9t^2 + 16t + .5
the t of the vertex is -16/(2(-4.9)) = 80/49
the h = -4.9(80/49) + 16(80/49) + .5
= appr 13.56 m