Answer:
The height of the ball is less than 17 feet for t > 2 seconds.
Step-by-step explanation:
The height of the ball after t seconds is given by the following equation:
[tex]h(t) = -16t^{2} + 81[/tex]
For which interval of the time is the height of the ball less than 17 feet
This is t for which:
[tex]h(t) < 17[/tex]
So
[tex]-16t^{2} + 81 < 17[/tex]
[tex]16t^{2} < -64[/tex]
Multiplying by -1
[tex]16t^{2} > 64[/tex]
[tex]t^{2} > \frac{64}{16}[/tex]
[tex]t^{2} > 4[/tex]
[tex]t > \sqrt{4}[/tex]
[tex]t > 2[/tex]
The height of the ball is less than 17 feet for t > 2 seconds.
