A 61.3 kg astronaut is on a space walk when
the tether line to the shuttle breaks. The
astronaut is able to throw a 11.0 kg oxygen
tank in a direction away from the shuttle with
a speed of 10.6 m/s, propelling the astronaut
back to the shuttle.
Assuming that the astronaut starts from
rest, find the final speed of the astronaut after
throwing the tank.
Answer in units of m/s
To find the final speed of the astronaut after throwing the tank, we can use the principle of conservation of momentum.
The total momentum before the tank is thrown is zero since the astronaut is at rest. After throwing the tank, the total momentum should still be zero because no external forces are acting on the system. Therefore, the momentum gained by the astronaut in the opposite direction should be equal to the momentum lost by the tank.
The formula for momentum is:
Momentum = mass * velocity
Let's label the mass of the astronaut as ma and the mass of the tank as mt. The initial velocity of the astronaut is zero, and the final velocity of the tank is also zero (since it is thrown away). The final velocity of the astronaut, vf, is what we want to find.
Using the conservation of momentum, we can write the equation:
ma * 0 + mt * 0 = ma * vf + mt * 0
Since both terms on the left side of the equation are zero, we can simplify it further:
0 = ma * vf
Rearranging the equation, we can find the final velocity of the astronaut:
vf = 0 / ma
Since anything divided by zero is undefined, the final velocity of the astronaut is zero.
Therefore, the final speed of the astronaut after throwing the tank is 0 m/s.