Answer:
The arrow will hit the ground approximately 10.5 seconds after launch.
Step-by-step explanation:
The arrow experiments a free fall motion, which is a particular form of uniform accelerated motion due to gravity and in which air friction and effects from Earth's rotation can be neglected. Then, the height as a function of time (
), measured in feet, is obtained by the following kinematic formula:
(1)
Where:
- Initial height of the arrow, measured in feet.
- Initial velocity of the arrow, measured in feet per second.
- Time, measured in seconds.
- Gravitational acceleration, measured in feet per square second.
If we know that
,
,
and
, then the following polynomial is obtained:
(2)
Lastly, we find the roots of the given expression by the Quadratic Formula:
and ![t_{2} \approx -0.207\,s](https://tex.z-dn.net/?f=t_%7B2%7D%20%5Capprox%20-0.207%5C%2Cs)
Time is a positive variable and then we conclude that the only solution that is physically reasonable is approximately 10.526 seconds.
The arrow will hit the ground approximately 10.5 seconds after launch.