Question

A 95-kg astronaut and a 1300-kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.17 m/s directly away from the shuttle. Seven-and-a-half seconds later the astronaut comes into contact with the shuttle.

What was the initial distance from the shuttle to theastronaut?

Answer 1

`d=17.44 m`

Step-by-step explanation:

Conservation of Momentum. Momentum is said to be conserved when there is zero net external force acting on the object.

So mathematically:

Definition of momentum:
`p = m*v`

Newton's 1st law:
`F = m*a` ⇒
`m*(dv)/(dt)=(dp)/(dt)`

Net external force is zero:
`F = 0`⇒
`(dv)/(dt)=0`=Dp=0

Conservation of Momentum is mathematically expressed as:

mv(initial) = mv(final)

Hence in this case:

`v=0.17 (m)/(s)`

by conservation of energy:

`m_(s)*v_(s)=m_(a)*v_(a)`

`1300kg*0.17 (m)/(s)=95kg*m_(a)`

`m_(a)=2.326(m)/(s)`

`m_(a)=(d)/(t)`

`d=m_(a)*t`

`d=2.32(m)/(s)*7.5s`

`d=17.44 m`