Answer:
The ball will be at a height of 3 feet above the ground after 3.729 seconds.
Step-by-step explanation:
Let suppose that the tennis player has hit the ball vertically, meaning that ball will experiment a free fall, that is, an uniform accelerated motion due to gravity. The time taken by the ball in terms of its initial velocity ([tex]v_{o}[/tex]), in feet per second, initial position ([tex]x_{o}[/tex]), in feet, final position ([tex]x[/tex]), in feet, and gravitational acceleration ([tex]g[/tex]), in feet per square second is described by this second order polynomial:
[tex]x = x_{o} + v_{o}\cdot t + \frac{1}{2}\cdot g\cdot t^{2}[/tex] (1)
If we know that [tex]x_{o} = x = 3\,ft[/tex], [tex]v_{o} = 60\,\frac{ft}{s}[/tex] and [tex]g = -32.174\,\frac{ft}{s^{2}}[/tex], then the time needed by the ball to be at a height of 3 feet again is:
[tex]3\,ft = 3\,ft + \left(60\,\frac{ft}{s} \right)\cdot t + \frac{1}{2}\cdot \left(-32.174\,\frac{ft}{s^{2}} \right)\cdot t^{2}[/tex]
[tex]-16.087\cdot t^{2}+60\cdot t = 0[/tex] (2)
[tex]t^{2} - 3.729\cdot t = 0[/tex]
[tex]t \cdot (t -3.729) = 0[/tex]
The binomial contains the time when the ball will be at a height of 3 feet again. In other words, the ball will be at a height of 3 feet above the ground after 3.729 seconds.
