Electromagnetic waves and astronaut

[yogi41]

Homework Statement

I've been trying to do this problem for about 2 hours now. I can't seem to find the right equations to use. Any help would be appreciated

A spacewalking astronaut servicing an orbiting space telescope has run out of fuel for her jet pack and is floating 20.0 m from the space shuttle with zero velocity relative to the shuttle. The astronaut and all her gear have a total mass of 150kg. If she uses her 220w flashlight as a "light rocket," how long will it take her to reach the shuttle?

Homework Equations

The Attempt at a Solution

 

[Dick]

How about this one, E=c*p. Where E is the energy of the light beam, p is it's momentum and c=speed of light.

 

[yogi41]

the answer is supposed to be 25.1 hours. When i used E=c*p i ended up getting 1250000 hours. Am i doing a simple calculation wrong?

 

[Dick]

I get the 25 hour figure as well. Did you compute the force exerted by the beam? What are some of your intermediate results?

 

[yogi41]

well i first calculated p 220w/3x10^8 which was 7.33 x 10^-7
then i divided that answer by 150kg to get 4.89 x 10^-9 which I'm assuming is my velocity
from there i divided the distance from the ship which was 20m to get 2.44 x 10^-10
and then i divided 1/2.44 x 10^-10 to get my answer in seconds

 

[Dick]

Keep track of units. Then you won't have to 'assume' that something is a velocity. Power/c is a force. (Power/c)/mass is an acceleration. Not a velocity.

 

[yogi41]

so I took the square root of the 2.44 x 10^-10 1/s^2 to get 1.56 x 10^-5 1/s and i flipped the sign by 1/1.56 x 10^-5 1/s to get 64018.4 but then when i convert it back to hours it's only 17.8 hours when it is supposed to be 25.1 hours. Where did i make the mistake? thanks for the help

 

[Dick]

The relation between distance, time and acceleration is d=(1/2)*a*t^2. Looks like you dropped the (1/2).