Problem from the text: A photon-powered spacecraft of mass 10.0kg emits radiatio

Question

Problem from the text:

A photon-powered spacecraft of mass 10.0kg emits radiation of wavelenght 225nm with a power of 1.50kW in the backward direction. To what speed will it have accelerated after 10 years if relased into free space?

m=10 kg
P=1.50kW = 1.5*103J/s
t=10years=3.16*108s

=225nm=225*10-9m

Using the reasoning from the solved problem on this site:

Why did they use the speed of light and not calculate for the accleration (a)!

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This is how I would derive the equation for the problem:

F=ma and using Newtions second law we know that F=p/t (assuming that p does not change, p1=p2 and t=10 years)

p=mv and using the debroglie relation (=h/p) we can derive: p=h/

If entered the units in I belive I end up with ms-2.

Is this the correct method/derived formulat? (my final answer for the problem is a=9.32*10-37)

Explanation / Answer

To calculate the initial momentum of thespacecraft

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