Explanation:
The situation described here is parabolic movement. However, as we are told the instrument is thrown upward from the surface, we will only use the equations related to the Y axis.
In this sense, the main movement equation in the Y axis is:
[tex]y-y_{o}=V_{o}.t-\frac{1}{2}g.t^{2}[/tex] (1)
Where:
[tex]y[/tex] is the instrument's final position
[tex]y_{o}=0[/tex] is the instrument's initial position
[tex]V_{o}=15m/s[/tex] is the instrument's initial velocity
[tex]t[/tex] is the time the parabolic movement lasts
[tex]g=2.5\frac{m}{s^{2}}[/tex] is the acceleration due to gravity at the surface of planet X.
As we know [tex]y_{o}=0[/tex] and [tex]y=0[/tex] when the object hits the ground, equation (1) is rewritten as:
[tex]0=V_{o}.t-\frac{1}{2}g.t^{2}[/tex] (2)
Finding [tex]t[/tex]:
[tex]0=t(V_{o}-\frac{1}{2}g.t^{2})[/tex] (3)
[tex]t=\frac{2V_{o}}{g}[/tex] (4)
[tex]t=\frac{2(15m/s)}{2.5\frac{m}{s^{2}}}[/tex] (5)
Finally:
[tex]t=12s[/tex]
