A 62.6 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 13.3 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.

This is conservation of momentum, first law. There is no net force on the astronaut - bottle system and the initial momentum is zero so:

0 = mass astronaut* velocity astronaut + mass bottle * velocity bottle

Well, let's calculate that, shall we?

First, let's find the momentum of the oxygen tank before it is thrown. The momentum of an object is given by the equation:

momentum = mass × velocity

So, the momentum of the oxygen tank before it is thrown is:

momentum = (mass of the oxygen tank) × (velocity of the oxygen tank)

momentum = (11.0 kg) × (13.3 m/s)

Now, since momentum is conserved in a closed system (such as an astronaut and the oxygen tank in space), the total momentum after the tank is thrown should be equal to the total momentum before the tank is thrown.

Let's say the final velocity of the astronaut is v (in m/s). Since the astronaut starts from rest, his initial momentum is zero.

So, the total momentum after the tank is thrown is:

momentum of the astronaut after throwing the tank = (mass of the astronaut) × (final velocity of the astronaut)

momentum of the astronaut after throwing the tank = (62.6 kg) × (v)

Since momentum is conserved, we can set the two momentum equations equal to each other:

(mass of the oxygen tank) × (velocity of the oxygen tank) = (mass of the astronaut) × (final velocity of the astronaut)

(11.0 kg) × (13.3 m/s) = (62.6 kg) × (v)

Now, let's solve for v:

v = [(11.0 kg) × (13.3 m/s)] / (62.6 kg)

v ≈ 2.34 m/s

So, the final speed of the astronaut after throwing the tank is approximately 2.34 m/s.

Just a reminder, always practice safe tethering!

To find the final speed of the astronaut after throwing the tank, we can use the principle of conservation of momentum.

The initial momentum of the system (astronaut + oxygen tank) is zero because the astronaut is at rest. After throwing the tank, the momentum of the system is still zero because there is no external force acting on it.

The momentum of an object is given by the formula:

momentum = mass × velocity

Let's denote the mass of the astronaut as "m1" and the mass of the oxygen tank as "m2". The initial momentum of the system is:

initial momentum = m1 × 0 + m2 × 0

Since the initial momentum is zero, the final momentum of the system after the astronaut throws the tank must also be zero:

final momentum = m1 × final velocity1 + m2 × final velocity2

We know the mass of the astronaut is 62.6 kg (m1) and the mass of the oxygen tank is 11.0 kg (m2). We also know the mass of the astronaut is much larger than the mass of the tank, so the final velocity of the tank (final velocity2) will be much larger than the final velocity of the astronaut (final velocity1).

Therefore, we can approximate the final velocity of the astronaut as:

final velocity1 ≈ - (m2 × final velocity2) / m1

Plugging in the values:

final velocity1 ≈ - (11.0 kg × 13.3 m/s) / 62.6 kg

final velocity1 ≈ - 2.344 m/s

Since the final velocity of the astronaut should be in the opposite direction to the initial direction, the magnitude of the final velocity is:

final velocity = |final velocity1| ≈ 2.344 m/s

So the final speed of the astronaut after throwing the tank is approximately 2.344 m/s.

To find the final speed of the astronaut after throwing the tank, we need to 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.

The momentum (p) of an object is given by the product of its mass (m) and velocity (v):

p = m * v

Before the throw, the astronaut is at rest, so their momentum is zero:

p_astronaut_initial = m_astronaut * v_astronaut_initial = 0

After the throw, the astronaut acquires a velocity (v_astronaut_final) in the opposite direction of the thrown tank. The momentum of the tank (p_tank) is given by:

p_tank = m_tank * v_tank

The total momentum after the throw is:

p_total_final = p_astronaut_final + p_tank

Since the momentum is conserved, we have:

p_total_initial = p_total_final

Since the astronaut is initially at rest, the total momentum before the throw is simply the momentum of the tank:

p_total_initial = p_tank

Substituting the momentum equations:

m_tank * v_tank = m_astronaut_final * v_astronaut_final + m_tank * v_tank

Rearranging the equation to solve for the final velocity of the astronaut:

m_astronaut_final * v_astronaut_final = 0,
v_astronaut_final = -m_tank * v_tank / m_astronaut_final

Plugging in the given values:

m_astronaut_final = 62.6 kg,
m_tank = 11.0 kg,
v_tank = 13.3 m/s

v_astronaut_final = -11.0 kg * 13.3 m/s / 62.6 kg

v_astronaut_final = -2.3427 m/s

Since we are interested in the magnitude of the final velocity, we disregard the negative sign:

Final speed of the astronaut after throwing the tank = |v_astronaut_final| = 2.3427 m/s.