Answer:
Time, t = 4.5 s
Step-by-step explanation:
The number of seconds t it takes the ball to hit the green can be represented by the equation :
[tex]-16t^2 + 70t + 5 = -4[/tex]
It means that the initial velocity is 70 ft/s. The above equation becomes:
[tex]-16t^2 + 70t + 9=0[/tex]
It is required to find the time taken by the ball to land on the ground. It is a quadratic equation. The solution of quadratic equation is given by :
[tex]t=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\\\\t=\dfrac{-b+ \sqrt{b^2-4ac} }{2a},\dfrac{-b- \sqrt{b^2-4ac} }{2a}\\\\t=\dfrac{-70+ \sqrt{(70)^2-4\times (-16)(9)} }{2(-16)}, \dfrac{-70-\sqrt{(70)^{2}-4\times(-16)(9)}}{2(-16)}[/tex]
t = −0.125 and t = 4.5 s
Time cannot be negative. So, the time taken by the ball to land on the ground is 4.5 seconds.
