Astronaut and Wrench Momentum Problem

[ommnomnomnom]

Homework Statement

An astronaut of mass 76.0 kg is taking a space walk to work on the International Space Station. Because of a malfunction with the booster rockets on his spacesuit, he finds himself drifting away from the station with a constant speed of 0.530 m/s. With the booster rockets no longer working, the only way for him to return to the station is to throw the 7.75 kg wrench he is holding.

(a) In which direction should he throw the wrench?

(b) He throws the wrench with speed 14.32 m/s with respect to himself.
After he throws the wrench, how fast is the astronaut drifting toward the space station?

(c) What is the speed of the wrench with respect to the space station?

Homework Equations

Conservation of momentum
mu = mv

The Attempt at a Solution

Part (a) is easy, the answer is "away from the station".

Now I'm stuck in the last 2 parts.

I'm using (+) for toward the space station.

For (b), I did:
m_w*u_w + m_a*u_a = m_w*v_w + m_a*v_a
u_w and u_a are both -0.53 m/s, right?

(7.75 kg + 76 kg) * -0.53 m/s = 7.75 kg * -14.32 m/s + 76 kg * v_a
v_a = 0.8762 m/s
After I submit this, it says:
Your response differs from the correct answer by more than 10%. Double check your calculations.

For (c), I did:
Velocity of Astronaut wrt Station: v_SA = 0.530 m/s
Velocity of Wrench wrt Astronaut: v_AW = 14.32 m/s
So, velocity of wrench wrt station should be:
v_SW = v_SA + v_AW
v_SW = 0.530 + 14.32 = 14.85 m/s
After I submit this, it says:
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.

 

[rl.bhat]

Hi ommnomnomnom, welcome to PF.

(7.75 kg + 76 kg) * -0.53 m/s = 7.75 kg * -14.32 m/s + 76 kg * v_a

The astronaut and wrench must move in the opposite direction. So their velocities cannot have the same sign.

 

[ommnomnomnom]

Hi ommnomnomnom, welcome to PF.

(7.75 kg + 76 kg) * -0.53 m/s = 7.75 kg * -14.32 m/s + 76 kg * v_a

The astronaut and wrench must move in the opposite direction. So their velocities cannot have the same sign.

Are you talking about v_w and v_a?
I put negative 14.32 m/s for v_w.
For v_a, I got a positive 0.8762 m/s.