posted by Z
A lunar lander in powered descent at 100 m above the surface of the moon slows down from a velocity of 20 m/s to 0.5 m/s at constant acceleration. Assume that the lander has a mass of 20,000 kg and that burning the fuel does not change the mass. Answer the following questions.
What is the acceleration of the lander?
How long will it take the lander to change velocity from 20 m/s to 0.5 m/s?
What is the thrust (T) of the engines?
I will have to assume that it goes the entire 100 meters during this deceleration and crashes into the moon at .5 m/s
-.5 = -20 + a t
100 = -20 t + .5 a t^2
a = (-.5+20)/t
-100 = -20 t + .5 (20-.5) t
100 = 20 t -9.75 t
t = 9.75 seconds to slow down (part b)
a = +2 up (part a)
I assume gravity is earth /6 = 9.81/6 = 1.635
force up = Thrust = T
force down = m g = 20,000 (1.635)
= 32700 Newtons
F = m a
T - 32700 = 20000(2)
T = 72700 Newtons