Question

A NASA explorer spacecraft with a mass of 1,000 kg takes off in a positive direction from a stationary asteroid. If the velocity of the spacecraft is 250 m/s and the asteroid is pushed back –25 m/s, what is the mass of the asteroid? Assume there is no net force on the system.

Answer 1

Answer: 10,000 kg

Explanation:

Here, the concept used is 'Law of Conservation of Momentum'.

i.e. m1v1 = m2v2

Now,

m1 = 1000 kg

v1 = 250 m/s

m2 = ?

v2 = -25 m/s [-'ve sign shows direction of motion of asteroid is opposite to direction of spacecraft]

Therefore,

m2 = (1000 x 250)/25

= 10,000 kg

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Answer 2

By using final momentum formula we get the value of, the mass of the asteroid is 909.09 kg.

• The conservation of momentum principle, which asserts that a system's overall momentum remains constant in the absence of a net external force, can be used to resolve this issue.

• Let's use the letters "m" and "v" to represent the asteroid's mass and starting velocity, respectively.
• Initial momentum is determined by multiplying the system's start velocity by the sum of the system's initial masses (spacecraft plus asteroid).
• We may simplify the initial momentum to: as we know the mass of the spacecraft is 1 kg and the system's speed is 0 m/s before takeoff.

        initial momentum = m x v

• When the spacecraft lifts off, the system's momentum is:

        Final momentum = mass of spacecraft x final velocity of spacecraft +                        mass of asteroid x final velocity of asteroid

• We are aware that the spacecraft's ultimate velocity is 250 m/s and that its mass is still 1,000 kg.
• The asteroid's ultimate velocity is -25 m/s since we also know that it is pushed back with a velocity of -25 m/s.
• The ultimate momentum may now be reduced to:

       Final momentum = 1000 kg x 250 m/s + m x (-25 m/s)

       Final momentum = 250,000 kgm/s - 25ms

• Given that the system's momentum is known to be conserved, we may set the beginning momentum to be equal to the end momentum:

        m x v = 250,000 kg m/s - 25ms

     Now, we can determine the asteroid's mass:

      m x v + 25m = 250,000 kg m/s

      m x (v + 25) = 250,000 kg m/s

      m = 250,000 / (v + 25)

     By substituting given values we get:

     m = 250,000 kg m/s / (250 m/s + 25 m/s)

      m = 909.09 kg

      As a result, the asteroid's mass is quite close to 909.09 kg.

For similar question on final momentum,

https://brainly.in/question/33882056

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