Answer:
Step-by-step explanation:
The height of the ball after t seconds is represented by, [tex]h(t) = -16t^{2} + 42t[/tex]
Putting h(t) = 5, we get
[tex]5 = -16t^{2} + 42t\\16t^{2} - 42t + 5 = 0\\16t^{2} - 40t - 2t + 5 = 0\\2t\times(8t - 1) -5\times(8t - 1) = 0\\(8t - 1)(2t - 5) = 0\\t = \frac{1}{8}, \frac{5}{2}[/tex]
At [tex]t = \frac{1}{8}[/tex] the ball was moving upward, since [tex]\frac{1}{8} < \frac{5}{2}[/tex].
It will be downward at [tex]t = \frac{5}{2} = 2.5[/tex]
The player intercept the ball after 2.5 seconds of the kick.
