Aquarterback throws a football to a teammate.The football is 6.5ft above the ground when it leaves the quarterback's hand. His teammate catches it 3.5s later, at a height above the ground of 5 ft. Projectile motion formula h(t)=-16t^2+vt+h_(0) h_(0)=6.5 v=? h=5 when t=3.5 Determine the value of v,rounded to the nearest whole number. vapprox 20 XLongrightarrow 56 COMPLETE Which quadratic equation models the situation correctly? h(t)=-16t^2+61 h(t)=-16t^2+202.5 h(t)=-16t^2+56t+5 A h(t)=-16t^2+56t+6.5

## Step 1<br />The problem involves the physics concept of projectile motion. The formula for the height of a projectile at any given time is given by:<br />### \(h(t) = -16t^2 + vt + h_0\)<br />where \(h(t)\) is the height of the projectile at time \(t\), \(v\) is the initial velocity, and \(h_0\) is the initial height.<br /><br />## Step 2<br />We are given that the football is thrown from a height of 6.5 feet (\(h_0 = 6.5\)) and it lands at a height of 5 feet (\(h = 5\)) after 3.5 seconds (\(t = 3.5\)). We are asked to find the initial velocity (\(v\)).<br /><br />## Step 3<br />We can substitute the given values into the formula to solve for \(v\):<br />### \(5 = -16(3.5)^2 + v(3.5) + 6.5\)<br /><br />## Step 4<br />Solving this equation for \(v\) gives us the initial velocity.<br /><br />## Step 5<br />The quadratic equation that models the situation correctly is the one that matches the initial height, the final height, and the time it takes for the football to reach the final height.