An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws a #9 kg# object at a speed of #3/4 m/s#, how much will his speed change by?

Question

An astronaut with a mass of #75 kg# is floating in space.  If the astronaut throws a #9 kg# object at a speed of #3/4 m/s#, how much will his speed change by?

Olivia Askew · Accepted Answer

The change in the speed of the astronaut is #=0.09ms^-1#

We have conservation of momentum

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

The mass of the astronaut is #m_1=75kg#

The mass of the object is #m_2=9kg#

As the astronaut is floating in space initially,

#u_1=u_2=0ms^-1#

The speed of the object is #v_2=3/4ms^-1#

Therefore,

#75v_1+3/4*9=0#

The speed of the astronaut is #v_1=-3/4*1/75*9=-0.09ms^-1#

Nathan Ashcroft · Answer

undefined To find the change in the astronaut's speed, we can use the principle of conservation of momentum. The initial momentum of the astronaut and the object combined is equal to the final momentum after the object is thrown.

Initial momentum = (mass of astronaut * initial speed of astronaut) + (mass of object * initial speed of object)

Final momentum = (mass of astronaut * final speed of astronaut) + (mass of object * final speed of object)

Using the conservation of momentum:

Initial momentum = Final momentum

(75 kg * 0 m/s) + (9 kg * 3/4 m/s) = (75 kg * final speed of astronaut) + (9 kg * final speed of object)

Solving for the final speed of the astronaut:

(9 kg * 3/4 m/s) = (75 kg * final speed of astronaut)

Final speed of astronaut = (9 kg * 3/4 m/s) / 75 kg

Final speed of astronaut ≈ 0.09 m/s

Therefore, the astronaut's speed will change by approximately 0.09 m/s.