Answer:
[tex]3.7\ \text{m/s}^2[/tex]
[tex]7.4\ \text{N}[/tex]
4 m
[tex]3397678.06\ \text{m}[/tex]
[tex]1.55\times 10^{14}\ \text{N}[/tex]
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 6=0t+\dfrac{1}{2}\times a\times1.8^2\\\Rightarrow a=\dfrac{6\times2}{1.8^2}\\\Rightarrow a=3.7\ \text{m/s}^2[/tex]
The acceleration due to gravity (g) on Mars is [tex]3.7\ \text{m/s}^2[/tex]
Weight is given by
[tex]w=mg\\\Rightarrow w=2\times 3.7\\\Rightarrow w=7.4\ \text{N}[/tex]
Weight of the stone on Mars is [tex]7.4\ \text{N}[/tex]
On Earth
[tex]v^2-u^2=2as\\\Rightarrow u=\sqrt{v^2-2as}\\\Rightarrow u=\sqrt{0-2\times-9.81\times1.5}\\\Rightarrow u=5.42\ \text{m/s}[/tex]
On Mars
[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0-(5.42)^2}{2\times -3.7}\\\Rightarrow s=4\ \text{m}[/tex]
A person could jump 4 m on Mars.
Acceleration due to gravity on planet is given by
[tex]g=\dfrac{GM}{R^2}\\\Rightarrow R=\sqrt{\dfrac{GM}{g}}\\\Rightarrow R=\sqrt{\dfrac{6.674\times 10^{-11}\times 6.4\times 10^{23}}{3.7}}\\\Rightarrow R=3397678.06\ \text{m}[/tex]
Radius of Mars is [tex]3397678.06\ \text{m}[/tex]
Gravitational force is given by
[tex]F=\dfrac{GMm}{r^2}\\\Rightarrow F=\dfrac{GM(M\times 3\times 10^{-9})}{r^2}\\\Rightarrow F=\dfrac{6.674\times 10^{-11}\times (6.4\times 10^{23})^2\times 3\times 10^{-9}}{(2.3\times 10^7)^2}\\\Rightarrow F=1.55\times 10^{14}\ \text{N}[/tex]
The force of gravity between Mars and Deimos is [tex]1.55\times 10^{14}\ \text{N}[/tex]
