Question

An 80 kg astronaut has gone outside his space capsule to do some repair work. Unfortunately, he forgot to lock his safety tether in place, and he has drifted 5.0 m away from the capsule. Fortunately, he has a 950 W portable laser with fresh batteries that will operate it for 1.0 hr. His only chance is to accelerate himself toward the space capsule by firing the laser in the opposite direction. He has a 8.3 hr supply of oxygen. How long will it take him to reach the capsule?

I got an answer of 9.15 hours, but somehow this is incorrect... what could i have done wrong?

Answer 1

here,

mass of the asternaut , m = 80 kg

distance travelled , d = 5 m

power , P = 950 W

time of operation , t = 1 hr = 3600 s

Force , F = P/c

F = 950 /( 3* 10^8)

F = 3.17 * 10^-6 N

accelration , a = F/m = 3.96 * 10^-8 m/s^2

when accelrating,

the distance trvaelled , d' = 0.5 * a*t^2 = 0.5 * 3.96 * 10^-8 * 3600^2

d'= 0.2565 m

final velocity , v = a*t

v = 3.96 * 10^-8 * 3600

v = 1.4256 * 10^-4 m/s

for the remainig disatnce let the time taken be t'

t' = (d - d1)/v

t' = ( 5 - 0.2565)/( 1.4256 * 10^-4)

t' = 9.24 hours

the time taken to reach the capsule is 10.24 h