In an unusual return to space, Astronaut Sally Ride is conducting repair work on the Hubble Space telescope. She throws a hammer of mass 500.0g forward at 20.0m/s. The astronaut, mass 80.0kg, recoils in the opposite direction. What is Sally's recoil velocity?

v2 =m1•v1/m2 =0.5•20/80 =0.125 m/s

To find Sally's recoil velocity, we need to apply the law of conservation of momentum. According to this law, the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting.

Let's consider the initial momentum and the final momentum in this scenario. Initially, only the hammer is in motion, and Sally is at rest. After throwing the hammer, both Sally and the hammer are in motion but in opposite directions.

The initial momentum (before the throw) is given by the equation:

Initial momentum = hammer momentum + Sally's initial momentum

The hammer's momentum can be calculated using the formula:

Momentum = mass x velocity

Given:
Hammer mass (m1) = 0.5 kg
Hammer velocity (v1) = 20 m/s

So, the hammer's momentum is:

Hammer momentum = m1 x v1

Next, let's calculate Sally's initial momentum. Since she is at rest initially, her momentum is zero (m2 x v2 = 0).

Therefore, the initial momentum is equal to the hammer's momentum:

Initial momentum = Hammer momentum + Sally's initial momentum
Initial momentum = m1 x v1 + m2 x v2
Initial momentum = m1 x v1 + 0 (as Sally is at rest initially)
Initial momentum = m1 x v1

Now, let's find the final momentum (after the throw). The final momentum is given by:

Final momentum = hammer momentum + Sally's final momentum

We're looking for Sally's recoil velocity, so let's represent her final velocity as v3.

The final momentum is equal to:

Final momentum = m1 x v1 + m2 x v3

Since there is no external force, the initial momentum is equal to the final momentum:

Initial momentum = Final momentum

Therefore, we have:

m1 x v1 = m1 x v1 + m2 x v3

Let's solve for v3 (Sally's recoil velocity):

v3 = (m1 x v1)/m2

Given:
m1 = 0.5 kg (hammer mass)
v1 = 20 m/s (hammer velocity)
m2 = 80 kg (Sally's mass)

Plugging the values into the equation:

v3 = (0.5 kg x 20 m/s) / 80 kg

v3 ≈ 0.125 m/s

Therefore, Sally's recoil velocity is approximately 0.125 m/s in the opposite direction to the hammer's throw.