Assume that we are on Planet-I and a rocketof mass 4350 kg is projected vertically upwardfrom the surface of this planet.It stops at apoint 9360 km from the surface of the planet.Find the kinetic energy of the rocket imme-diately after it is fired of
Assume that we are on Planet-I and a rocket
of mass 4350 kg is projected vertically upward
from the surface of this planet.It stops at a
point 9360 km from the surface of the planet.
Find the kinetic energy of the rocket imme-
diately after it is fired off.The radius of this
planet is 2340 km,the gravitational accelera-
tion at the surface is 7.28 m/s2,and the grav-
itational constant 6.67259 × 10−11 Nm2/kg2.
The gravitational acceleration decreases as
the rocket travels away from Planet-I.
Answer in units of J
Gravitational force:
F = G*m*M/r^2
At r = 2340,000 m
F/m = G*M/2340,000^2 = 7.28
GM = 3.986*10^13
At the highest point,all kinetic energy is transfered to potential energy.Therefore,
Ek = integral F dr from r0 to (r0+9.460*10^6)
= G*m*M[1/r0 - 1/(r0+9.460*10^6)]
= 3.986*10^13 (4350,000)[1/2340,000 - 1/11800,000]
= 5.941*10^13 J
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