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posted by  Learning on 6/5/2007 3:52:20 PM  |  status: Live  

Magnitude of thrust - Physics 7th Ed. Cutnell Ch.4 #93

Course Textbook Chapter Problem
Algebra Based Physics Physics 7th Ed Cutnell 4 93
Question Details:
A 1.14 x 10 (to the power of 4) kg lunar landing craft is about to touch down on the surface of the moon, where the acceleration due to gravity is 1.60 m/s2.  At an altitude of 165 m the craft's dwonward velocity is 18.0 m/s.  To slow down the craft, a retrorocket is firing to provide an upward thrust.  Assuming the descent is vertical, find the magnitude of the thrust needed to reduce the velocity to zero at the instant when the craft touches the lunar surface.
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posted by HungryHungryHippo on 6/5/2007 4:27:57 PM  |  status: Live
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Learning's comment:
"Aha!! Thank you!"
Response Details:
The total force required to accelerate (actually decelerate) the craft so that it slows down the landing craft to a stop over 165 meters can be found using the equation (vertically up is positive):

vf2 = vi2 + 2ad

vf = 0
vi = -18 m/s
d = -165 m
a = ?

0 = (-18)2 + 2a(-165)
-2a(-165) = 324
a = 0.98 m/s2

The total force is therefore equal to:

Ftotal = ma = (1.14x104kg)(0.98m/s2) = 1.12x104 N

Ftotal = Fthrust - Fcraft
Fthrust = Ftotal + Fcraft
Fthrust = 1.12x104 N + (1.14x104kg)(1.60m/s2)
Fthrust = 2.94x104 N
Hope I have helped.  Anyone feel free to correct any mistake I may have made.
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