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(D) The power of the light beam is $P = 10$ $W$. The energy emitted in time $t$ is $E = P 	imes t = 10t$.The momentum $p$ carried by the light beam i

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$2.4 	imes 10^9$ s

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(D) The power of the light beam is $P = 10$ $W$. The energy emitted in time $t$ is $E = P 	imes t = 10t$.The momentum $p$ carried by the light beam is given by $p = E/c$,where $c = 3 	imes 10^8$ m/s is the speed of light.According to the law of conservation of momentum,the momentum acquired by the astronaut must be equal to the momentum of the light beam: $M 	imes v = p$.Given $M = 80$ kg and $v = 1$ m/s,we have $80 	imes 1 = \frac{10t}{3 	imes 10^8}$.Solving for $t$: $t = \frac{80 	imes 3 	imes 10^8}{10} = 24 	imes 10^8 = 2.4 	imes 10^9$ s.

An astronaut floating freely in space decides to use his flashlight as a rocket. He shines a $10$ $W$ light beam in a fixed direction so that he acquires momentum in the opposite direction. If his mass is $80$ kg,how long must he shine the light to reach a velocity of $1$ $m/s$?

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