An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws a #7 kg# object at a speed of #4 m/s#, how much will his speed change by?

1 Answer
May 13, 2018

His/her speed decreases by #0.37# meters per second.

Explanation:

Using conservation of momentum, which states that,

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

where:

  • #m_1,m_2# are the masses of the two objects

  • #u_1,u_2# are the initial velocities of the two objects

  • #v_1,v_2# are the final velocities of the two objects

I will assume that both the astronaut and the object are stationary and have no initial velocity whatsoever.

#:.75 \ "kg"*0 \ "m/s"+7 \ "kg"*0 \ "m/s"=75 \ "kg"*v_1+7 \ "kg"*4 \ "m/s"#

#75 \ "kg"*v_1=-28 \ "kg m/s"#

#v_1=(-28color(red)cancelcolor(black)"kg""m/s")/(75color(red)cancelcolor(black)"kg")#

#~~-0.37 \ "m/s"#

So, the astronaut's velocity will be #0.37 \ "m/s"# opposite to their original direction, or their speed will decrease by #0.37 \ "m/s"#.