Answer: 191.8 feet
Explanation:
The equation for the ball's height h at time t seconds after launch is h(t) = -16t^2 + 1.6t + 190.4.
To find the maximum height the ball achieves before landing, we need to find the maximum value of h(t). To do this, we need to find the vertex of the parabola represented by the equation. The vertex of a quadratic equation in the form of y = a(x-h)^2 + k is (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
We can find the x-coordinate of the vertex by using the formula:
h = -b/2a
Here, a = -16, b = 1.6, and c = 190.4
Plugging these values into the formula:
h = -1.6/2*(-16) = 1/8
The x-coordinate of the vertex is 1/8 of a second, which is the time at which the ball reaches its maximum height.
To find the y-coordinate of the vertex, we can plug in the value of t = 1/8 into the equation for h(t):
h(1/8) = -16(1/8)^2 + 1.6(1/8) + 190.4
This gives us the maximum height that the ball achieves before landing, which is approximately 191.8 feet.