An astronaut holds a rock 100 m above surface of Planet X. The rock is then thrown upwards with a sleek of 15m/s. The rock reaches the ground 10s after it is thrown the atmosphere of Planet X has a negligible effect on the rock. Determined the acceleration due to gravity of the rock when it is in planet x

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Question:

An astronaut holds a rock 100 m above surface of Planet X. The rock is then thrown upwards with a sleek of 15m/s. The rock reaches the ground 10s after it is thrown the atmosphere of Planet X has a negligible effect on the rock. Determined the acceleration due to gravity of the rock when it is in planet x

Answer:[tex]5 m/s^{2}[/tex]Explanation:This problem is related to vertical motion, and the equation that models it is:[tex]y=y_{o}+V_{o}sin\theta t-\frac{1}{2}gt^{2}[/tex] (1)Where:[tex]y=0m[/tex] is the rock's final height[tex]y_{o}=100 m[/tex] is the rock's initial height[tex]V_{o}=15 m/s[/tex] is the rock's initial velocity[tex]\theta=90\°[/tex] is the angle at which the rock was thrown (directly upwards)[tex]t=10 s[/tex] is the time[tex]g[/tex] is the acceleration due gravity in Planet XIsolating [tex]g[/tex] and taking into account [tex]sin(90\°)=1[/tex] :[tex]g=(-\frac{2}{t^{2}})(y-y_{o}-V_{o}t)[/tex] (2)[tex]g=(-\frac{2}{(10 s)^{2}})(0 m-100 m-(15 m/s)(10 s))[/tex] (3)[tex]g=5 m/s^{2}[/tex] (4) This is the acceleration due gravity in Planet X

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