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A space probe is traveling in outer space with a momentum that has a magnitude of 5.92 x 107 kg·m/s. A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of 1.91 x 106 N and a direction opposite to the probe's motion. It fires for a period of 10.4 s. Determine the momentum of the probe after the retrorocket ceases to fire.

Answer :

Answer:

[tex]p_f=7.90\times 10^7\ kg.m/s[/tex]

Explanation:

Given that,

Initial momentum of the probe, [tex]p_i=5.92\times 10^7\ kg.m/s[/tex]

Applied force to the probe, [tex]F=1.91\times 10^6\ N[/tex]

Time period, T = 10.4 s

To find,

Final momentum of the probe.

Solution,

We know that according to the impulse- momentum theorem, the impulse is equal to the change in momentum. Mathematically, it is given by :

[tex]F\Delta t=p_f-p_i[/tex]

[tex]p_f=F\Delta t+p_i[/tex]

[tex]p_f=1.91\times 10^6\times 10.4+5.92\times 10^7[/tex]

[tex]p_f=7.90\times 10^7\ kg.m/s[/tex]

Therefore, the momentum of the probe after the retrorocket ceases to fire is [tex]7.90\times 10^7\ kg.m/s[/tex]. Hence, this is the required solution.

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