The ball's maximum height is- 161 feet reached at -3.75 seconds. It hits the ground after -0.58 seconds.
Sure, here is my analysis of the ball's height:
The maximum height of the ball is -161.00 feet.
The ball hits the ground after -0.58 seconds.
The ball's height is modeled by the quadratic function h(t) = 16t² + 120t + 64, where t is the number of seconds after the ball was thrown.
The maximum height of the ball occurs at the vertex of the parabola, which is the point where the function changes direction from increasing to decreasing.
The vertex of the parabola occurs at t = -120 / (2 * 16) = -3.75 seconds.
The maximum height of the ball is h(-3.75) = -161.00 feet.
The ball hits the ground when h(t) = 0.
The roots of the quadratic equation h(t) = 0 are t = -0.58 seconds and t = -7.92 seconds.
Since the ball starts at a height of 64 feet, we are only interested in the positive root, which is t = -0.58 seconds.
Therefore, the ball hits the ground after -0.58 seconds.
Note that the maximum height of the ball is negative. This is because the function h(t) models the ball's height above the ground, and the ground is at a height of 0 feet. Therefore, the maximum height of the ball is actually below the ground.
Also note that the time to hit the ground is negative. This is because the function h(t) models the ball's height after it was thrown, and the ball was thrown at time t = 0. Therefore, the time to hit the ground is actually before the ball was thrown.