c 0 and5.625 sec represent the times when the ball is on the ground, first when the player kicks the ball, then when the ball lands.
a We are given the equation h=-16t^2+90t, with h as the balls height after t seconds. For this part, we need to know the height of the ball after one second. Let's substitute and find h.
After one second, the ball will be 74 feet off the ground.
b Since this is a quadratic equation, we can use the vertex of the parabola as a maximum point. The first step in finding the vertex is to find the axis of symmetry for the function h= -16t^2+ 90t
Since the question asks for time to get to the maximum, we do not need the other coordinate of the vertex. It takes the ball about 2.8 seconds to reach it's maximum height.
c The most common way to find the amount of time it takes to reach 0 ft is the let h=0 and solve for t.
The ball is 0 ft off the ground at 0 sec and at about 5.6 sec. These represent the times the ball is on the ground, first when the player kicks the ball, then when the ball lands.
Alternative Solution
Using Reasoning
In Part B, we determined that the ball takes about 2.8 sec to reach the vertex. Since the parabola is symmetric about the axis of symmetry, we know that it will take the same amount of time again to get back to the same height.
2.8 * 2 = 5.6
The player kicked it from ground level, 0 ft off the ground, so we know it will reach ground level again after 5.6 seconds.
