A 64.3 kg astronaut is on a space walk when the tether line to the shuttle breaks. The astronaut is able to throw a 10.0 kg oxygen tank in a direction away from the shuttle with a speed of 11.9 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.
conservation of momentum
10*11.9+64.3V=0
solve for V.
1.85*
To find the final speed of the astronaut after throwing the tank, we can use the principle of conservation of momentum. According to this principle, the total momentum before the throw is equal to the total momentum after the throw.
Let's denote the mass of the astronaut as "m1", initial velocity as "v1", mass of the tank as "m2", and final velocity of the astronaut as "v2".
We're given:
m1 = 64.3 kg (mass of astronaut)
v1 = 0 m/s (initial velocity of astronaut)
m2 = 10.0 kg (mass of oxygen tank)
v2 (final velocity of astronaut, which we need to find)
The momentum of an object is given by the product of its mass and velocity:
momentum = mass × velocity
Before the throw, the total momentum is:
(total momentum)before = (momentum of astronaut)before + (momentum of tank)before
= m1 × v1 + m2 × 0 (since the tank is at rest before the throw)
= m1 × v1
After the throw, the total momentum is:
(total momentum)after = (momentum of astronaut)after + (momentum of tank)after
= m1 × v2 + m2 × 11.9 m/s
Since the total momentum is conserved, we have:
(total momentum)before = (total momentum)after
Therefore:
m1 × v1 = m1 × v2 + m2 × 11.9 m/s
Since the astronaut starts from rest (v1 = 0), the equation simplifies to:
0 = m1 × v2 + m2 × 11.9 m/s
Now we can solve for v2:
m1 × v2 = - m2 × 11.9 m/s (we multiply by -1 to move m2 to the other side of the equation)
v2 = (- m2 × 11.9 m/s) / m1
Substituting the given values:
v2 = (- 10.0 kg × 11.9 m/s) / 64.3 kg
Calculating this expression:
v2 ≈ -1.85 m/s (rounded to two decimal places)
The negative sign indicates that the final velocity of the astronaut is in the opposite direction of the initial velocity (since the astronaut is propelled back towards the shuttle). Therefore, the magnitude of the final velocity is 1.85 m/s.
So, the final speed of the astronaut after throwing the tank is approximately 1.85 m/s.