Answer: 7.436 s
Explanation:
This situation is related to vertical motion, specifically free fall and can be modelled by the following equation:
[tex]y=y_{o}+V_{o} t+\frac{gt^{2}}{2}[/tex]
Where:
[tex]y= 0m[/tex] is the final height of the object (when it makes splash)
[tex]y_{o}=271 m[/tex] is the initial height of the object
[tex]V_{o}=0 m/s[/tex] is the initial velocity of the object (it was dropped)
[tex]g=-9.8m/s^{2}[/tex] is the acceleration due gravity (directed downwards)
[tex]t[/tex] is the time since the objecct is dropped until it makes splash
[tex]0=y_{o}+0+\frac{gt^{2}}{2}[/tex]
Clearing [tex]t[/tex]:
[tex]t=\sqrt{\frac{-2y_{o}}{g}}[/tex]
[tex]t=\sqrt{\frac{-2(271 m)}{-9.8m/s^{2}}}[/tex]
Finally:
[tex]t=7.436 s[/tex]
