Answer:
the time taken by the astronaut to reach safety = 9.8 hr
Explanation:
The equation for intensity can be written as :
where :
Replacing that into the above previous equation; we have:
However ; the force needed to push the astronaut is as follows:
F = ma
where ;
m = mass of the astronaut and a = its acceleration
we as well say;
Replacing P with 1000 W ; m with 80 kg and for c
Then; a =
a =
It is also known that the battery will run for one hour and after which the battery on the laser will run out
Then to determine the change in the position after the first hour ; we have:
= 0.27 m
Furthermore, the final velocity of the astronaut is determined as:
where ;
replacing and a =
; Then:
Also; when he drifted 5.0 m away from the capsule; the distance is far short of the 5 m but he still have 9 hours left of oxygen . In addition to that, he acceleration is also zero and the final velocity remains the same, so:
To find the final distance traveled by the astronaut ;we have:
where;
= the final distance
d = total distance
So;
The time taken to reach the final distance can be calculated as:
where;
= is the time to reach the final distance
Replacing 4.73 for and
m/s for
We knew the laser was operated for 1 hour; thus the total time taken by the astronaut to reach the final distance is the sum of the time taken to reach the final distance and the operated time of the laser.
Hence ; the time taken by the astronaut to reach safety = 9.8 hr