A question on momentum conservation of bodies in combined motion

[internationallove089]

TL;DR Summary

momentum conservation, newton's laws

Frictions are neglected in the system pictured. Here, a 1kg object released from above moves the car underneath. When this object falls off the car, what is its speed in m/s?

This question was asked from momentum conservation, but I didn't want to do it from there. Can you solve the question from momentum conservation first? Secondly, the answer in my solution is not included in the options..

I find the answer to be 0.29 m/s.

 

[kuruman]

You should try momentum and mechanical energy conservation because it is the easier approach to this problem. Note that momentum is conserved in the horizontal direction but not the vertical. Once you have seen how the answer is put together, you can then try sorting out the kinematics equations and free body diagrams.

Whichever way you try to solve this, use symbols instead of numbers to keep track of what you are doing and helps us figure out where you went wrong in case you need additional help. Also, please take some time to learn how to use LaTeX to post your equations. Click on the link "LaTeX Guide" above the "Attach files" button.

 

[internationallove089]

You should try momentum and mechanical energy conservation because it is the easier approach to this problem. Note that momentum is conserved in the horizontal direction but not the vertical. Once you have seen how the answer is put together, you can then try sorting out the kinematics equations and free body diagrams.

Whichever way you try to solve this, use symbols instead of numbers to keep track of what you are doing and helps us figure out where you went wrong in case you need additional help. Also, please take some time to learn how to use LaTeX to post your equations. Click on the link "LaTeX Guide" above the "Attach files" button.

The objects move together, so we need to find the speed of the object as it leaves the end of the car to solve for conservation of momentum. But for this, we need to determine the final speed in the system in which they move together..

 

[kuruman]

The objects move together, so we need to find the speed of the object as it leaves the end of the car to solve for conservation of momentum. But for this, we need to determine the final speed in the system in which they move together..

"Move together" means that one does not move relative to the other and they have the same velocity and acceleration. If the block falls off the wedge, it does "move together" with the block. It moves separatly from the block with its own velocity and acceleration down the incline. The wedge on wheels moves with horizontal velocity and acceleration to the right.