Answer:
The initial height of the sandbox before being released is 219.272 meters.
Explanation:
The sandbag is accelerated until hitting the ground due to the effect of gravitation, since height is too small with respect to the radius of Earth, then gravity acceleration can be considered constant and due to this, the following kinematic equation is applied to determine the initial height as a function of time:
[tex]y = y_{o} + v_{o}\cdot t + \frac{1}{2}\cdot a \cdot t^{2}[/tex]
Where:
[tex]y[/tex] - Final height, measured in meters.
[tex]y_{o}[/tex] - Initial height, measured in meters.
[tex]v_{o}[/tex] - Initial speed, measured in meters per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]a[/tex] - Acceleration, measured in meters per square second.
Now, the initial height is cleared:
[tex]y_{o} = y - v_{o}\cdot t - \frac{1}{2}\cdot a \cdot t^{2}[/tex]
Given that [tex]y = 0\,m[/tex], [tex]v_{o} = 3\,\frac{m}{s}[/tex], [tex]t = 7\,s[/tex] and [tex]a = -9.807\,\frac{m}{s^{2}}[/tex], the initial height of the sandbox is:
[tex]y_{o} = 0\,m - \left(3\,\frac{m}{s} \right)\cdot (7\,s) - \frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (7\,s)^{2}[/tex]
[tex]y_{o} = 219.272\,m[/tex]
The initial height of the sandbox before being released is 219.272 meters.
