Two astronauts are floating out in space. Initially they are at rest 20.0 m apar

Question

Two astronauts are floating out in space. Initially they are at rest 20.0 m apart. Sandra & her suit have a mass of 100kg; George & his suit have a mass of 140kg. What is the acceleration of each astronaut? Assume the acceleration were constant. Estimate how long would it take before Sandra and George meet. Treat them like point masses. (Careful, they BOTH accelerate so the total distance they both move must be 20.0m). Give your answer in standard time units of years, months, days, hours, and minutes. Would the actual time be more than or less than this? Explain.

Explanation / Answer

part a:

force between the two astronauts=universal gravitational constant*mass of first astronaut*mass of second astronaut/distance ^2

=6.674*10^(-11)*100*140/20^2=2.3359*10^(-9) N

acceleration of sandra=force/mass=2.3359*10^(-11) m/s^2

acceleration of George=force/mass=1.6685*10^(-11) m/s^2

part :

let they take t seconds to meet.

then distance travelled by sandra+distance travelled by george=20

==>0.5*acceleration of sandra*time^2+0.5*acceleration of george*time^2=20

==>0.5*(2.3359*10^(-11)+1.6685*10^(-11))*t^2=20

==>t=999450.4533 seconds

part c:

actual time will be less than this as force will increase as distance decreases.

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