A softball pitcher throws a softball to a catcher behind home plate. The softball is 3 feet above the ground when it leaves the pitcher's hand at a velocity of 50 feet per second . If the softball's acceleration is -16ft/s^2 which quadratic equation models the situation correctly? h(t)=at^2+vt+h_(0) h(t)=50t^2-16t+3 h(t)=-16t^2+50t+3 3=-16t^2+50t+h_(0) 3=50t^2-16t+h_(0)

## Step1: Identify the problem type### The problem involves modeling the motion of a projectile (softball) with specified initial conditions using a quadratic equation. This falls under the category of kinematics in calculus.## Step2: Determine the general form of the motion equation### The general form of a quadratic equation for the height of the projectile as a function of time is given by \(h(t) = a t^{2} + v t + h_{0} \), where represents acceleration, is the initial velocity, and is the initial height.## Step3: Substitute given values into the equation### From the problem statement: initial height feet, initial velocity feet/second, and acceleration feet/second .### Substituting these values, the equation becomes \( h(t) = -16 t^2 + 50 t + 3 \).#