an astronaut on a space walk discovers that this jet pack has no longer works, leaving him stranded 50m from the space-craft. If the jet pack is removable, explain how the astronaut can still use it to return to the ship?

Throw it in the direction opposite from the ship. Let momentum be conserved :)

Well, in this situation, the stranded astronaut can try a little DIY rocket science. If the jet pack is removable, it still has some useful components like fuel tanks, thrusters, and controls. The astronaut can gather all these parts and, using their amazing space skills, MacGyver themselves a makeshift propulsion system.

Now, remember, I'm just a Clown Bot, not an actual astronaut, but I've heard that using a wrench, duct tape, and some spare parts, they can fashion a new connection for the jet pack thrusters to the astronaut's spacesuit, essentially turning themselves into a makeshift human rocket.

With a little bit of luck and a whole lot of trust in their makeshift contraption, the astronaut can activate the DIY propulsion system and fly back safely to the space-craft, making for quite the unconventional and entertaining rescue mission. Just be sure to invite me to the iCircus show when they get back to Earth!

To use the non-functioning jet pack to return to the spacecraft, the astronaut can follow these steps:

1. Assess the condition of the jet pack: Check if any parts of the jet pack are still functioning or if it can be repaired. This will help determine the next course of action.

2. Remove the jet pack: If the jet pack is removable, detach it from the spacesuit and handle it carefully.

3. Use the jet pack as a propulsion tool: Turn on the jet pack and use it to propel yourself towards the spacecraft. Even if it doesn't provide the intended thrust for space travel, it can still generate some maneuvering force.

4. Orient yourself towards the spacecraft: Determine the direction in which the spacecraft is located and align yourself accordingly. This will ensure that you are moving in the right direction.

5. Control the movement: Use small bursts or controlled thrust from the jet pack to guide yourself towards the spacecraft. This will help you maintain stability and control over your movement.

6. Monitor the distance: Pay attention to your progress towards the spacecraft. Observe the distance diminishing as you get closer to your objective. Adjust your movements accordingly.

7. Reach out for assistance: Once you are close enough to the spacecraft, reach out for assistance from your crew members or use any available handholds or attachment points to secure yourself to the spacecraft.

Note: It is essential to remember that this solution assumes the astronaut has knowledge and training in handling jet packs and the associated risks.

To use the non-functional jet pack to return to the ship, the astronaut can follow these steps:

1. Assess the situation and ensure personal safety: The astronaut should make sure they are secured to the spacecraft or have a firm grip on something to prevent drifting away in zero gravity.

2. Verify that the jet pack is removable: The astronaut needs to confirm that the jet pack can be detached from their spacesuit. If it is not removable, they will need to consider alternative options for returning to the ship.

3. Apply minimal thrust from the jet pack: Even if the jet pack is not working, it can still provide a small amount of propulsion due to the residual gas remaining in the system. The astronaut should push or kick off gently from a stable position using the jet pack to start moving towards the spacecraft.

4. Use body movements for propulsion: The astronaut can use their arms and legs to push and pull against the jet pack while floating in space. Tugging, pushing, and kicking motions can help generate momentum and slowly propel them towards the ship.

5. Plan the trajectory: The astronaut should determine the most efficient path towards the ship by considering the distance, obstacles, and any other constraints in the surroundings. Adjusting body angles and using slight twists or spins can help redirect the direction of movement.

6. Utilize objects or other tools: If there are any nearby objects, the astronaut can grab onto them or use them as leverage to gain additional propulsion. Tools such as grappling hooks or retractable cords can be employed to latch onto the spacecraft or any other stationary object, aiding in the return journey.

7. Conserve energy: Returning to the ship using makeshift propulsion techniques can be physically demanding. The astronaut should be mindful of conserving energy, taking periodic breaks to rest and regain strength.

8. Communicate and seek assistance: While the astronaut is making their way back to the ship, they should maintain communication with their crewmates inside the spacecraft. This will enable them to coordinate efforts, seek guidance, or explore other options for rescue if needed.

It is important to note that the feasibility of using a non-functional jet pack to return to the ship depends on various factors, including the astronaut's position, available tools, and the specific conditions of the spacewalk. The astronaut should consider their training, experience, and the advice provided by mission control in such a situation.