Answer:240.1 m
Step-by-step explanation:
We are given the following equation that models the the time it takes to an object to fall to the ground:
[tex]t_{(H)}=\sqrt{\frac{2H}{g}}[/tex]
Where:
[tex]t_{(H)}=7 s[/tex] is the time it takes to the object to fall to the ground
[tex]H[/tex] is the object's initial height
[tex]g=9.8 m/s^{2}[/tex] is the acceleration due gravity
Isolating [tex]H[/tex]:
[tex]t^{2}=(\sqrt{\frac{2H}{g}})^{2}[/tex]
[tex]t^{2}=\frac{2H}{g}}[/tex]
[tex]H=\frac{t^{2}g}{2}[/tex]
Solving with the given data:
[tex]H=\frac{(7 s)^{2}(9.8 m/s^{2})}{2}[/tex]
[tex]H=240.1 m[/tex] This is the initial height
