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)

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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)

Answer 1

### \( h(t) = -16 t^{2} + 50 t + 3 \)

Answer 2

## 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 \(a\) represents acceleration, \(v\) is the initial velocity, and \(h_{0}\) is the initial height. ## Step3: Substitute given values into the equation ### From the problem statement: initial height \(h_{0} = 3 \) feet, initial velocity \( v = 50 \) feet/second, and acceleration \( a = -16 \) feet/second\(^2\). ### Substituting these values, the equation becomes \( h(t) = -16 t^2 + 50 t + 3 \). #

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