Answer:
The gain in gravitational potential energy is [tex]3.5\times10^{8}\ J[/tex].
Explanation:
Given that,
Mass of rocket = 1210 kg
Altitude = 203 km
Mass of the moon [tex]M=7.36\times10^{22}\ kg[/tex]
Radius [tex]r=1740\ km[/tex]
We need to calculate the gain in gravitational potential energy
Using formula of change in gravitational potential energy
[tex]\Delta P.E=P.E_{f}-P.E_{i}[/tex]
[tex]\Delta P.E=\dfrac{GMm}{R+h}-\dfrac{GMm}{R}[/tex]
[tex]\Delta P.E=GMm(\dfrac{1}{h}-\dfrac{1}{R+h})[/tex]
[tex]\Delta P.E=6.65\times10^{-11}\times7.36\times10^{22}\times1210(\dfrac{1}{1740\times10^{3}}-\dfrac{1}{203\times10^{3}+1740\times10^{3}})[/tex]
[tex]\Delta P.E=355597598.216\ J[/tex]
[tex]\Delta P.E=3.5\times10^{8}\ J[/tex]
Hence, The gain in gravitational potential energy is [tex]3.5\times10^{8}\ J[/tex].
