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## Homework Statement

A 50 g, 420 mw laser pointer is floating in outer space (don’t ask how it got there) at rest with respect to an observer. The laser pointer is turned on and let go. If the battery runs continuously for 250 hours before dying, what is the final speed achieved by the laser pointer with respect to the observer?

## Homework Equations

P=W/t (Power)

E

_{k}=pc

W=E

_{k}(conservation of energy)

n=v/c

p=mv(momentum)

## The Attempt at a Solution

Since it is in space, I can say that n=1 so v=c(it is essentially in vacuum). From this I can derive that

W=E

_{k}

from the conservation of energy law. Knowing this I can replace

P=E

_{k}/t.

This is where I assume the question is non-relativistic which I am not sure if I can. Let's say I do make the assumption. I can then get

Pt= E

_{k}= pc

Pt = pc = mvc

v = Pt/mc

v = (420 * 10

^{-3}W) * (900,000 s)/(0.05 kg)(3.00 * 10

^{8}m/s)

=

**2.52 m/s**

I am pretty sure I can not say Pt = pc since pc is the energy for light and Pt is referring to the laser pointer itself but I am not sure what else to do

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