Hello!
Answer:
The arrow will hit the floor in 13,5 seconds.
Explanation:
For this exercise, we have a quadratic equation that is the way (for this exercise) to calculate the time when the arrow will hit the floor, it means that the h (y) will be 0.
We have the following equation:
[tex]h=-16 t^{2} +Vo.t+h0[/tex]
This is a quadratic equation, so we are going to use the next formula:
[tex]\frac{-b+- \sqrt{ b^{2}-(4).(a).(c} }{2.(a)}[/tex]
Substituting we have:
[tex]\frac{-214+- \sqrt{ 214^{2}-(4).(-16).(33)} }{2.(-16)}[/tex]
[tex]\frac{-214+- \sqrt{ 45796+2212} }{(-32)}=\frac{-214+- \sqrt{48008} }{(-32)} \\ =\frac{-214+-219,10 }{(-32)}[/tex]
We have 2 different results, we are looking for a positive result because we are calculating a time value.
Then:
[tex]t1=13,52s \\ t2=-0,17s[/tex]
So, we are choosing t1 because it's the positive result.
Finally, we have that the arrow will hit the floor in 13,5 seconds approximately.
Have a great day!
