Question

A punter kicked the football into the air with an upward velocity of 62 ft/s. It's height h in feet after t seconds is given by the function h = -16t^2 + 62t + 2. What is the maximum height the ball reaches? Show solutions,

Answer 1

To find the maximum height the ball reaches, we need to determine the vertex of the quadratic function h(t) = -16t^2 + 62t + 2. The vertex represents the highest point of the ball's trajectory.

The formula for the x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).

In this case, the function is h(t) = -16t^2 + 62t + 2, so we have a = -16 and b = 62.

Using the formula, we can calculate the t-coordinate of the vertex:

t = -b / (2a) t = -62 / (2(-16)) t = -62 / (-32) t = 1.9375

Now, substitute this value of t back into the original function to find the maximum height:

h = -16t^2 + 62t + 2 h = -16(1.9375)^2 + 62(1.9375) + 2 h ≈ 119.671875

Therefore, the maximum height the ball reaches is approximately 119.67 feet.