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

Answer:

velocity is 5 m/s

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

$(m + M)\times u = (m\times v_1) + (M\times v_2)$

Now insert values

$0 = (10 kg \times 50 m/s ) + (100 kg \: v_2)$

Further simplifying

$v_2=-\frac{500 kg-m/s}{100kg}$

So,

$v_2= -5\:m/s$

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