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I am looking for some help on the following problem:

http://img387.imageshack.us/img387/5481/problemuk7.jpg [Broken]

I have some questions on part (b)

Here is my solution for (a):

Conservation of linear momentum:

[tex]\Delta p = p_f - p_i = m_f v_f - m_i v_i [/tex]

Solving for mass:

[tex]E = mc^2 \Rightarrow m = \frac{E}{{c^2 }}[/tex]

Substituting mass into conservation of linear momentum:

[tex]

\Delta p = \frac{{E_f }}{{c^2 }} \cdot v_f - \frac{{E_i }}{{c^2 }} \cdot v_i

[/tex]

Replace final velocity and initial velocity with [tex]c[/tex] since both velocities are the speed of the photons which are constant speed of light:

[tex]\Delta p = \frac{{E_f }}{{c^2 }} \cdot c - \frac{{E_i }}{{c^2 }} \cdot c

[/tex]

Simplify:

[tex]\Delta p = \frac{{E_f }}{c} - \frac{{E_i }}{c}[/tex]

[tex]\Delta p = \frac{{\Delta E}}{c}[/tex]

I think I may have a solution for part (b):

Using the conservation of mechanical energy:

[tex]\Delta E_{internal} = \Delta K [/tex]

[tex]1500 = \frac{1}{2}mv^2 [/tex]

[tex]1500 = \frac{1}{2}\left( {1.5} \right)v^2 [/tex]

[tex]v = \sqrt {\frac{{1500}}{{\left( {0.5} \right)\left( {1.5} \right)}}}[/tex]

[tex]v = 44.7 \mbox{ m/s}[/tex]

Does that look like a valid solution for part (b)?

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# Momentum of flashlight in intergalactic space

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