Answer:
1.038s
Explanation:
To solve this problem we use the following equation for the free fall movement:
[tex]h=v_{i}t+\frac{1}{2} gt^2[/tex]
where [tex]h[/tex] is the height, [tex]v_{i}[/tex] is the initial velocity, in this case since the rock was just dropped, [tex]v_{i}=0[/tex], [tex]g[/tex] is the acceleration of gravity of the planet in this case mars, thus g will be: [tex]g=3.711 m/s^2[/tex]. And [tex]t[/tex] is time, wich is what we are looking for.
Clearing the equation for [tex]t[/tex] :
[tex]h=v_{i}t+\frac{1}{2} gt^2[/tex]
since [tex]v_{i}=0[/tex]
[tex]h=\frac{1}{2} gt^2[/tex]
[tex]\frac{2h}{g}=t^2[/tex]
[tex]\sqrt{\frac{2h}{g}}=t[/tex]
we have [tex]g=3.711 m/s^2[/tex] and from the problem we have that [tex]h=2m[/tex]
thus:
[tex]\sqrt{\frac{2(2m)}{3.711m/s^2}}=t[/tex]
[tex]\sqrt{\frac{4m}{3.711m/s^2} }=\sqrt{1.0779s^2}=1.038s[/tex]
The time it takes is 1.038s
