Answer:
2.54334 seconds
9.4364 m/s
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
M = Mass of Mars = [tex]6.419\times 10^{23}\ kg[/tex]
R = Radius of Mars = [tex]3.397\times 10^6\ m[/tex]
The acceleration due to gravity of a planet is given by
[tex]g=\frac{GM}{R^2}\\\Rightarrow g=\frac{6.67\times 10^{-11}\times 6.419\times 10^{23}}{(3.397\times 10^6)^2}\\\Rightarrow g=3.71024\ m/s^2[/tex]
Equation of motion
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 12=0t+\frac{1}{2}\times 3.71024\times t^2\\\Rightarrow t=\sqrt{\frac{12\times 2}{3.71024}}\\\Rightarrow t=2.54334\ s[/tex]
The time taken to fall 12 m in Mars is 2.54334 seconds
[tex]v=u+at\\\Rightarrow v=0+3.71024\times 2.54334\\\Rightarrow v=9.4364\ m/s[/tex]
The vertical velocity at impact is 9.4364 m/s
