Two astronauts are at rest in outer space, one 20.0 m from the Space Shuttle and

Question

Two astronauts are at rest in outer space, one 20.0 m from the Space Shuttle and the other 40.0 m from the shuttle. Using a 178.0-W laser, the astronaut located 40.0 m away from the Shuttle decides to propel the other astronaut toward the Space Shuttle. He focuses the laser on a piece of totally reflecting fabric on her space suit. If her total mass with equipment is 108.0 kg, how long will it take her to reach the Space Shuttle?

I tried this, but it was wrong. Where is the mistake?

P=T*178.0*2/c
therefore the force = P/T
=178.0*2/c
acceleration rate a=178.0*2/c*108
=1.098*10^-9
so we have
at^2/2= 20.0 m
so t = sqrt(20.0*2/a)
= 190799.61s

Explanation / Answer

The distance of the first astronaut, s1 = 20 m The distance of the second astronaut, s2 = 40 m The change in momentum of the photons are         P = T(178)(2/c) hence , force F = P/T                         = (178)(2/ c) from , Newton's second law of motion ,    force F = ma therefore ,     ma = (178)(2/ c) acceleration is       a = (178)(2/ mc)          = (178){2 / (108 kg)(3*108 m/s)}          = 1.098*10-8 m/s2 from kinematic equation ,            s = (1/2)at2   (20 m) = (1/2)(1.098*10-8 m/s2)(t)2 time t = 60357.16 s (or) (or)           ˜ 6.04*104 s

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