Derek kicks a soccer ball off the ground and in the air with an initial velocity of 31 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches?

Question

anonymous · Answer

This is a second degree polynomial. We know that second order polynomials have a parabolic shape when graphed. 

Imagine a parabola that opens downwards, the point where y is maximum is known as the vertex. The vertex of this equation can be found by using the following formula. First, find the time (the x-coordinate so to speak) at which the vertex occurs from $$t = {-b \over 2a}$$Then plug this value back into the equation to find the maximum height. 

Recall that second order polynomials have the form$$y = ax^2 + bx + c$$

Additionally, if you've taken calculus, you can take the first derivative, set it equal to zero, and solve for t. Then plug the found value of t back into the equation to find the maximum height. This is because the slop at the vertex is zero.

anonymous · Answer

$$v = -g \times t + v _{0} $$
$$t = v _{0}/g$$
$$\Delta y = - g \times t ^{2}/2 + v_{0}t$$

Replace t, g and initial velocity to find the maximum height.