Question

a ball is tossed into the air at 20 feet per second from a height of 7 feet. How long will it take the ball to reach the​ ground? Use the formula sequals negative 16 t squared plus v subscript o baseline t plus s subscript o​, where v subscript o baseline equals initial ​velocity, s subscript o equalsinitial ​altitude, and s equals altitude in feet after t seconds.

Answer 1

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:

$s(t)=-16t^{2}+v_{0}t+s_{0}$

Upon substituting the given values of initial velocity and initial altitude, we get:

$s(t)=-16t^{2}+20t+7$

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.

$-16t^{2}+20t+7=0$

Upon using quadratic formula, we get:

$t=\frac{-20\pm \sqrt{20^2-4\left(-16\right)7}}{2\left(-16\right)}\\t=\frac{5\pm\sqrt{53}}{8}$

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.