Answer:
Horizontal distance, d = 9.146
Step-by-step explanation:
The given function is
[tex]f(d) = -0.6d^{2} + 5.4d + 0.8[/tex]
The horizontal distance, d, is the distance on ground. So, set f(d) = 0.
That is, a height of zero which becomes the ground level.
[tex]0 = -0.6d^{2} + 5.4d + 0.8[/tex]
Using the quadratic formula:
[tex]d = \frac{-5.4±\sqrt{5.4^{2} -4(-0.6)(0.8)} }{2(-0.6)}\\ \\d = \frac{-5.4±\sqrt{29.16 + 1.92} }{-1.2}\\\\d = \frac{-5.4±\sqrt{31.08} }{-1.2} = d = \frac{-5.4±5.57}{-1.2}\\\\d = -0.146, 9.146[/tex]
Thus, the ball is in air between d=-0.146 to d=9.146.
Since the distance can not be negative, the ball remains in the air between d = 0 to d = 9.146.
Therefore d = 9.146
