Question

A 93 kg astronaut and a 1400 kg satellite are at rest relative tothe space shuttle. The astronaut pushes on the satellite, giving ita speed of 0.15 m/s directly away from the shuttle. Seven and ahalf seconds later the astronaut comes into contact with theshuttle.
What was the initial distance from the shuttle to theastronaut?

Answer 1

Answer:

16.93545 m

Explanation:

$m_1$ = Mass of astronaut = 93 kg

$m_2$ = Mass of satellite = 1400 kg

$v_1$ = Velocity of astrounaut

$v_2$ = Velocity of satellite = 0.15 m/s

As linear momentum of the system is conserved

$m_1v_1+m_2v_2=0\\\Rightarrow v_1=-\frac{m_2v_2}{m_1}\\\Rightarrow v_1=-\frac{1400\times 0.15}{93}\\\Rightarrow v_1=2.25806\ m/s$

As there is no acceleration

Distance = Speed × Time

$Distance=2.25806\times 7.5=16.93545\ m$

The initial distance from the shuttle to the astronaut is 16.93545 m