Answer:
The arrow reaches 400 feet in its way up at about 2.2 seconds after being launched.
Step-by-step explanation:
Since we want to find the time at which the arrow will reach 400 feet, we use this information in the equation for the height;
[tex]400=-16\,t^2+220\,t\\16\,t^2-220\,t+400=0[/tex]
and now use the quadratic equation to solve for the unknown time (t). Notice that been a quadratic equation we expect up to two answers, and then we will need to decide which answer to pick.
[tex]t=\frac{220}{2\,(16)} +/- \frac{\sqrt{(-220)^2-4 \,(16)(400)}}{2\,(16)} \\ \\t= 2.156\,sec\,\,\,or\,\,\, t=11.594\,sec[/tex]
This means that as the arrow goes up, it takes 2.156 seconds to reach 400 feet, and afterwards, after the arrow reaches it maximum height, it falls back due to acceleration of gravity, going through the same 400 feet height before reaching the ground.
We round the answer to the nearest tenth as requested.
