A lunar module (LM) lifts off from the lunar surface and flies a powered trajectory to its burnout point at 30 km altitude. The
velocity vector of the LM is parallel to the lunar surface at burnout. It then coasts halfway around the moon, where it must climb and rendezvous with the Apollo command module (CM) in a 250-km circular orbit. Note: μmoon = 4902.8 km3/s2, rmoon = 1740 km.a) Calculate vp, the burnout speed of the LM (km/s).b) Calculate vCM, the CM circular orbit speed (km/s).c) Calculate va, the LM orbit speed when it reaches the CM (km/s).d) Calculate the ∆v required to match speeds at the rendezvous with the CM (km/s).e) Calculate tcoast, the required coast time for the LM to reach the CM (seconds).f) In order to assure a rendezvous, it is desirable that the LM and CM arrive at the rendezvous point together. Where must the CM be in relation to the LM at burnout? Cite your answer as a time differential and an angle differential of the CM ahead of, or behind the LM burnout point. This sets the "launch window" for the LM takeoff.
1 answer:
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Answer:
a) Red: 1.34
Violet: 1.40
b) Red:
Violet:
Explanation:
a) We should use Snell's law to find the index of refraction:
with n1 the index of refraction of air, n2 the index of refraction of the glass, θi the angle of the incident ray respects the normal an θt the angle between the refracted ray an the normal. It's common to approximate n1=1
solving n2 for red light:
solving n2 for violet light:
b) Index of refraction on a medium is defined as the ratio between the velocity of electromagnetic waves on vacuum (velocity of light c) and the velocity in medium (v):
solving v for red:
solving v for violet
1) The mass of the continent is
2) The kinetic energy of the continent is 624 J
3) The speed of the jogger must be 4 m/s
Explanation:
1)
We start by finding the volume of the continent. We have:
is the side
is the depth
So the volume is
We also know that its density is
Therefore, we can find the mass by multiplying volume by density:
2)
The kinetic energy of the continent is given by:
where
is its mass
v = 3.2 cm/year is the speed
We have to convert the speed into m/s. We have:
3.2 cm = 0.032 m
So, the speed is:
So, we can now find the kinetic energy:
3)
Here we have a jogger of mass
m = 78 kg
And the jogger has the same kinetic energy of the continent, so
K = 624 J
The kinetic energy of the jogger is given by
where v is the speed of the jogger.
Solving for v, we find the speed that the jogger must have:
Learn more about kinetic energy:
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