An astronaut with a mass of #90 kg# is floating in space. If the astronaut throws a #20 kg# object at a speed of #6/5 m/s#, how much will his speed change by?

Question

An astronaut with a mass of #90 kg# is floating in space.  If the astronaut throws a #20 kg# object at a speed of #6/5 m/s#, how much will his speed change by?

Leo Abeyta · Accepted Answer

The change in the speed of the astronaut is #=0.27ms^-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=90kg#

The mass of the object is #m_2=20kg#

As the astronaut is floating in space initially,

#u_1=u_2=0ms^-1#

The speed of the object is #v_2=6/5ms^-1#

Therefore,

#90v_1+20*6/5=0#

The speed of the astronaut is #v_1=-24/(90)=-0.27ms^-1#

Layla Ahmed · Answer

undefined To calculate the change in the astronaut's speed, we can use the law of conservation of linear momentum. The initial momentum of the system (astronaut and object) is equal to the final momentum. The formula is Δv = Δp / m_astronaut, where Δp is the change in momentum and m_astronaut is the astronaut's mass.

Initial momentum = (mass_astronaut * initial speed_astronaut) + (mass_object * initial speed_object)
Final momentum = (mass_astronaut * final speed_astronaut) + (mass_object * final speed_object)

Δp = Final momentum - Initial momentum
Δv = Δp / m_astronaut