Suppose the mass of a fully loaded module in which astronauts take off from the moon is 10,000 kg. the thrust of its engines is 30,000 n. (a) calculate its the magnitude of acceleration in a vertical takeoff from the moon. (b) could it lift off from earth? if not, why not? if it could, calculate the magnitude of its acceleration.

Acceleration is the rate of change of velocity. The acceleration of the module is 1.365 m/s².

Given to us

Mass of the Module = 10,000 kg

The thrust of the engine, Fₓ = 30,000 N

A.)

We know in order to lift the module the thrust produced by the engine must be greater than the gravitational pull by the module. therefore,

where W is the weight of the moon,

Also, the acceleration on the moon is 1/6 of the acceleration on the earth,

We know that force is the product of mass and acceleration, therefore,

Hence, the acceleration of the module is 1.365 m/s².

B.)

If we need to lift the module on earth, we need a thrust that is greater than the weight of the module,

As the weight of the module is greater than the thrust produced by engines. therefore, the module can not take off from the earth.

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Part a)

a = 1.37 m/s/s

Part b)

since the force of gravity is more than the thrust force of rocket so it will not lift off the surface of Earth

Explanation:

Part a)

Net force on the Module due to thrust of engine is given as

now net force while is ejected out of the surface of moon is given as

here we know that

where we have

now the acceleration of the module on the moon is

Part b)

Now on the surface of earth the force of gravity on the module is given as

since the force of gravity is more than the thrust force of rocket so it will not lift off the surface of Earth

seeing the graph would

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s