We have been given that the ball is tossed into air at a speed of 20 feet per second and from a height of 7 feet.
We are supposed to use the formula:
[tex]s(t)=-16t^{2}+v_{0}t+s_{0}[/tex]
Upon substituting the given values of initial velocity and initial altitude, we get:
[tex]s(t)=-16t^{2}+20t+7[/tex]
We need to figure out the time that will take the ball to reach the ground. In order to do so, we will substitute s(t)=0 and solve for t.
[tex]-16t^{2}+20t+7=0\\[/tex]
Upon using quadratic formula, we get:
[tex]t=\frac{-20\pm \sqrt{20^2-4\left(-16\right)7}}{2\left(-16\right)}\\t=\frac{5\pm\sqrt{53}}{8}\\[/tex]
Upon finding the values of t using calculator, we get t=-0.285, 1.535
Therefore it will take the ball approximately 1.54 seconds to hit the ground.
