Idealist

A small spaceship whose mass is 1.5x10^3 kg (include-ing an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a 10 kW laser beam, what speed will the ship attain in 1.0 day because of the momentum carried away by the beam?

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shamim

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can u tell me the result option

Idealist

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The answer is 1.9 mm/s.

shamim

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ok

shamim

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i m trying

shamim

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i got the result velocity is 759 m/s

shamim

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should i explain my procedure

Idealist

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Yes, show me the work you did.

shamim

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ok i m showing

shamim

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let
m= mass
p=power
t=time
F=force
s= distance

shamim

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v=final velocity

shamim

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a= acceleration

shamim

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Now\[P=\frac{ W }{ t }=\frac{ Fs }{ t }=F\frac{ s }{ t }=Fv\]

Idealist

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What is the distance, s?

shamim

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\[or, 10000=Fv \]

shamim

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we know work= force* displacement or distaance

shamim

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or, \[F=10000/v\]

shamim

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now we know \[F=ma\]

shamim

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or, \[F=1500a\]

shamim

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or, \[10000/v=1500a\]

shamim

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r u getting my work

shamim

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or, \[a=10000/1500v\]

shamim

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now another law of motion is \[v=u+at=0+at=at=(10000/1500v) \times 24 \times 60 \times 60\]

shamim

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now solve it for v

Idealist

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Never mind. I found a formula for this problem, but thanks for the help.