Abaseball is thrown into the air from a height of 5 feet.The ball reaches a maximum height of 43 .5 feet and spends a tota of 3.2 seconds in the air. Which equation models the height of the baseball? Assume that acceleration due to gravity is an 16ft/s^2 h(t)=16t^2+49.64t+5 h(t)=-16t^2+5t+49.64 h(t)=-16t^2+49.64t+5 h(t)=16t^2+5t+49.64

## Step 1<br />The problem involves the physics of motion, specifically the motion of a projectile under the influence of gravity. The equation that models the height of the baseball is a quadratic equation, which is a common equation in physics problems involving motion.<br /><br />## Step 2<br />The general form of a quadratic equation is \(h(t) = at^2 + bt + c\), where \(a\), \(b\), and \(c\) are constants. In this case, the acceleration due to gravity is given as \(-16ft/s^2\), which is negative because it acts in the opposite direction to the upward motion of the ball.<br /><br />## Step 3<br />The maximum height of the ball is reached when the velocity is zero. This occurs at the vertex of the parabola represented by the quadratic equation. The time at which this occurs is given as \(t = 3.2\) seconds.<br /><br />## Step 4<br />The equation that models the height of the baseball is \(h(t) = -16t^2 + 49.64t + 5\). This equation is derived from the general form of a quadratic equation, with \(a = -16\), \(b = 49.64\), and \(c = 5\).