Question

A 100-kg astronaut floating in space holds a 10-kg object. Then the object is tossed at 50 m/s. How fast does the astronaut go after tossing the object?

Answer 1

velocity is 5 m/s

Step-by-step explanation:

mass of astronaut (M)=100kg

mass of object (m)=10kg

Initially they are rest , so initial velocity (u)= 0 m/s

Final velocity of object ;
`v_1=10m/s`

let final velocity of astronaut =
`v_2` (Unknown)

Now , By conservation of linear momentum

Initial momentum = Final momentum

`(m + M)* u = (m* v_1) + (M* v_2)`

Now insert values

`0 = (10 kg * 50 m/s ) + (100 kg \: v_2)`

Further simplifying

`v_2=-(500 kg-m/s)/(100kg)`

So,

`v_2= -5\:m/s`

So, velocity is 5 m/s (the negative sign is due to direction)