Question

An 80 kg astronaut has gone outside his space capsule to do some repair worlc Unfortunately, he forgot to lock his safetytether in place, and he has drifted 5.0 m away from the capsule. Fortunately, he has a 1000 w portable laser with freshbatteries that will operate it for 1.0 hr His only chance is to accelerate himself toward the space capsule by firing the laser inthe opposite direction. He has a 10-h supply of oxygen. How long will it take him to reach safety?

Answer 1

Step-by-step explanation:

Given

mass of astronaut m=80 kg

Drift d=5 m

Power P=1000 W

time allowed for laser t=1 hr

Force Provided by laser
`F=(Power)/(velocity)`

`F=(P)/(c)` , where c=velocity of light

acceleration
`a=(P)/(mc)`

Using Kinematic relation

`v=u+at`

here initial velocity is zero

`v=a* t`

`v=(P)/(mc)* t`

`v=(1000)/(80* 3* 10^8)* 3600`

`v=1.5* 10^(-4) s`

distance traveled

`x=ut+(1)/(2)at^2`

`x=(1)/(2)(P)/(mc)* t^2`

`x=0.5* (1000)/(80* 3* 10^8)* 3600^2`

`x=0.27 m`

Distance left to travel is d=5-0.27=4.73 m

Oxygen left for 9 hrs

time to cover 4.73 m

`time=(4.73)/(1.5* 10^(-4))`

`t=31,533.33 s`

`t=8.759 hr`

Therefore he will be able to cover 5 m before emptying cylinder