An 80kg astronaut, carrying a 20kg tool kit, is initially drifting towards a stationary space shuttle at a speed of 2 m/s. If he throws the toolkit towards the shuttle with a speed of 6 m/s as seen from the shuttle, what will his final speed be? Will it be toward or away from the shuttle?
Here, the velocities of the astronaut and his toolbox are to be measured relative to the shuttle. Assume the direction 'towards the shuttle' be positive.
Initially the toolbox and the astronaut are going towards the shuttle at a speed of 2 m/s. He is holding onto it; they are both moving together towards the shuttle.
Initial momentum = total mass*velocity
=` (80+20)*2 = 200` kgm/s
After the toolkit is thrown:
The momentum of the toolkit = `20*6 = 120` kgm/s
Let the final velocity of the astronaut be` v`
So, his momentum=`80*v` kgm/s
Hence, the final momentum after the throw=`(120+80v)` kgm/s
From the law of conservation of momentum:
The positive value of v indicates that his final speed is towards the shuttle.
Therefore, the final speed of the astronaut is 1 m/s towards the shuttle.