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)
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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
To determine the acceleration of the lander, we can use the equation:
Final velocity (v_f) = Initial velocity (v_i) + (acceleration * time)
By rearranging the equation, we can solve for acceleration:
Acceleration = (v_f - v_i) / time
Given that the final velocity (v_f) is 0.5 m/s, the initial velocity (v_i) is 20 m/s, and the time is unknown, we need to find the time it takes for the change in velocity.
To find the time it takes for the change in velocity, we can use the equation:
Change in velocity (Δv) = v_f - v_i
By rearranging the equation, we can solve for time:
Time = Δv / acceleration
Given that the change in velocity (Δv) is 0.5 m/s - 20 m/s = -19.5 m/s, and the acceleration is unknown, we can find the time it takes for the change in velocity.
To find the thrust (T) of the engines, we can use Newton's second law of motion:
Force (F) = mass (m) * acceleration
Since the mass of the lander is given as 20,000 kg and the acceleration is unknown, we can calculate the thrust of the engines.
Let's solve these step-by-step:
Step 1: Calculate the acceleration of the lander.
Acceleration = (v_f - v_i) / time
Acceleration = (0.5 m/s - 20 m/s) / time
Step 2: Calculate the time it takes for the change in velocity.
Time = Δv / acceleration
Time = (-19.5 m/s) / acceleration
Step 3: Calculate the thrust (T) of the engines.
Force = mass * acceleration
T = (20,000 kg) * acceleration
Given the information, let's proceed to solve step-by-step.
To find the acceleration of the lander, we can use the equation:
acceleration = (final velocity - initial velocity) / time
From the problem, we are given the final velocity (0.5 m/s) and the initial velocity (20 m/s), but we need to find the time it takes for the change in velocity.
To find the time taken, we can use the following kinematic equation:
final velocity = initial velocity + acceleration * time
Rearranging the equation to solve for time:
time = (final velocity - initial velocity) / acceleration
Now let's calculate the acceleration:
acceleration = (0.5 m/s - 20 m/s) / time
Next, we need to find the time it takes for the change in velocity:
time = (0.5 m/s - 20 m/s) / acceleration
However, we don't have the value of time yet. To find it, we need more information, specifically the time it takes for the lander to change velocity. Without that information, we cannot calculate the exact value of acceleration or time.
Regarding the thrust of the engines, we can use Newton's second law of motion, which states that the force applied is equal to mass multiplied by acceleration:
force (thrust) = mass * acceleration
Plugging in the known values:
force = 20,000 kg * acceleration
Since we don't have the exact value for acceleration, we cannot calculate the thrust of the engines at this point.