An astronaut with a mass of #80 kg# is floating in space. If the astronaut throws an object with a mass of #16 kg# at a speed of #3/8 m/s#, how much will his speed change by?
1 Answer
The speed of the astronaut changes by
Explanation:
This is a problem of momentum conservation, specifically an explosion. In an explosion, an internal impulse acts in order to propel the parts of a system into a variety of directions. This is often a single object, but can be, such as in this case, multiple objects which were initially at rest together. For collisions/explosions occurring in an isolated system, momentum is always conserved-no exceptions.
The Law of Conservation of Momentum:
#vecP_f=vecP_i#
For multiple objects,
#vecP=vecp_(t ot)=sumvecp=vecp_1+vecp_2+...vecp_n#
In our case, we have the momentum of the thrown object and the astronaut. We'll call the mass of astronaut
#m_1v_(1i)+m_2v_(2i)=m_1v_(1f)+m_2v_(2f)#
However, both the thrown object and the astronaut are initially at rest, so the total momentum before the "explosion" is
#0=m_1v_(1f)+m_2v_(2f)#
We can manipulate the equation to solve for
#v_(f1)=-(m_2v_(f2))/m_1#
Using our known values:
#v_(f1)=-((16kg)(3/8m/s))/(80kg)#
#=>v_(f1)=-3/40m/s=-0.075m/s#
In the above equations we've defined the direction that the object is thrown in as positive, so a negative answer tells us that astronaut moves in the opposite direction of the object. Because his initial velocity was
Hope this helps!