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

16.93545 m

Step-by-step 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=-(m_2v_2)/(m_1)\\\Rightarrow v_1=-(1400* 0.15)/(93)\\\Rightarrow v_1=2.25806\ m/s`

As there is no acceleration

Distance = Speed × Time

`Distance=2.25806* 7.5=16.93545\ m`

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