1) A 1500kg rocket is launched directly upward from the surface of the moon with

Question

1) A 1500kg rocket is launched directly upward from the surface of the moon with an initial speed of 1000m/s.(R=1.74x10^6 m; M=7.36x10^22 kg). Assume the rocket achieves this speed directly on the surface, and burns all its fuel in the process. The moon has no atmosphere, and ignore rotation.
a) how much work is done by the gravitational force from the moment of launch to its maximum altitude? B) calculate the max height above the surface of the moon that the rocket achieves. C) in general, if a mass m as launched directly upward with an initial speed v above a spherical planet of mass M and radius R, detrrmine the max height ( in terms of m, M, R and G) 1) A 1500kg rocket is launched directly upward from the surface of the moon with an initial speed of 1000m/s.(R=1.74x10^6 m; M=7.36x10^22 kg). Assume the rocket achieves this speed directly on the surface, and burns all its fuel in the process. The moon has no atmosphere, and ignore rotation.
a) how much work is done by the gravitational force from the moment of launch to its maximum altitude? B) calculate the max height above the surface of the moon that the rocket achieves. C) in general, if a mass m as launched directly upward with an initial speed v above a spherical planet of mass M and radius R, detrrmine the max height ( in terms of m, M, R and G) 1) A 1500kg rocket is launched directly upward from the surface of the moon with an initial speed of 1000m/s.(R=1.74x10^6 m; M=7.36x10^22 kg). Assume the rocket achieves this speed directly on the surface, and burns all its fuel in the process. The moon has no atmosphere, and ignore rotation.
a) how much work is done by the gravitational force from the moment of launch to its maximum altitude? B) calculate the max height above the surface of the moon that the rocket achieves. C) in general, if a mass m as launched directly upward with an initial speed v above a spherical planet of mass M and radius R, detrrmine the max height ( in terms of m, M, R and G) 1) A 1500kg rocket is launched directly upward from the surface of the moon with an initial speed of 1000m/s.(R=1.74x10^6 m; M=7.36x10^22 kg). Assume the rocket achieves this speed directly on the surface, and burns all its fuel in the process. The moon has no atmosphere, and ignore rotation.
a) how much work is done by the gravitational force from the moment of launch to its maximum altitude? B) calculate the max height above the surface of the moon that the rocket achieves. C) in general, if a mass m as launched directly upward with an initial speed v above a spherical planet of mass M and radius R, detrrmine the max height ( in terms of m, M, R and G)
a) how much work is done by the gravitational force from the moment of launch to its maximum altitude? B) calculate the max height above the surface of the moon that the rocket achieves. C) in general, if a mass m as launched directly upward with an initial speed v above a spherical planet of mass M and radius R, detrrmine the max height ( in terms of m, M, R and G)

Explanation / Answer

Ve= sqrt(2GM/R) = sqrt((2*6.67*10^-11*7.36*10^22)/(1.74*10^6)) = 2375.43 m/s

Since vi < ve , vf=0m/s

a) W= ½*m*(vf^2-vi^2) = ½*1500*(0^2-1000^2) = -7.5*10^8 J

b) Use law of conservation of energy,

KEf+PEf   = KEi+PEi

½*m*vf^2 – GMm/ Rf = ½*m*vi^2 - GMm/Ri

½*vf^2 – GM/Rf = ½*vi^2 - GM/Ri

½*(vf^2-vi^2) = GM(1/Rf-1/Ri)

½*(0^2-1000^2)= 6.67*10^-11*7.36*10^22(1/Rf-1/(1.74*10^6))         => Rf= 2.115*10^6 m

h = Rf-Ri = 2.115*10^6 – 1.74*10^6 = 375000 m = 375 km

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