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Alika [10]
4 years ago
13

Can we use momentum to see how fast the earth is going?

Physics
1 answer:
Kisachek [45]4 years ago
6 0

Yes, if we know the Earth's mass

Explanation:

The momentum of an object is a vector quantity given by the equation

p=mv

where

m is the mass of the object

v is its velocity

In this case, we are asked if we can find the velocity of the Earth by starting from its momentum. Indeed, we can. In fact, we can rewrite the equation above as

v=\frac{p}{m}

Therefore, if we know the momentum of the Earth (p) and we know its mass as well (m), we can solve the formula to find the Earth's velocity.

Learn more about momentum:

brainly.com/question/7973509

brainly.com/question/6573742

brainly.com/question/2370982

brainly.com/question/9484203

#LearnwithBrainly

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Answer:

a

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b

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Explanation:

Considering question a

From the question we are told that

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Generally given that the rocket burns all it fuel in a single stage , the final velocity of the rocket is mathematically represented as

          v_f = v_{ex}  ln [\frac{m_o}{m_k} ]

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        m_k =  m_o- m

=>      m_k =  m_o  -0.6m_o

=>    m_k =   [1-  0.6] m_o

=>      v_f = v_{ex}  ln [\frac{m_o}{[1 - 0.6]m_o} ]    

=>      v_f = 0.916 v_{ex}

Considering question b

From the question we are told that

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    The mass of the fuel at the second stage is  m_f = 0.3m_o

Generally the  velocity of the rocket at the first stage  is mathematically represented as

           v_i = v_{ex} * ln [ \frac{m_o }{[1- m]m_o } ]

=>         v_i = v_{ex} * ln [ \frac{m_o }{[1- 0.3]m_o } ]

=>         v_i = v_{ex} * ln [ \frac{1 }{0.7 } ]  

=>         v_i =0.357 v_{ex}

Generally the mass of the rocket after first stage is  

    m_r  =  m_o - 0.3m_o -0.1m_o

=>   m_r  =  0.6m_o

Generally the final  velocity of the rocket at the second stage is  

     v_f = v_i + v_{ex} * ln [\frac{m_r}{ m_f } ]

=>   v_f = v_i + v_{ex} * ln [\frac{0.6 m_o }{0.3mo } ]

=>   v_f = 0.357 v_{ex}  + 0.693 v_{ex}

=>   v_f = 1.05 v_{ex}

 

4 0
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