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## Homework Statement

On flat surface there is small cart m and big, initally resting ramp with mass m and height h.

a) At what speed should the cart travel to roll on the flat area on top of the ramp and stop relativly to it?

b) Assuming that cart moves with speed greater than calculated in a) what is the distance d between it and ramp when the it hits the ground?

Friction, air resistance and moment of inertia of the wheels of ramp and cart are neglible. Cart does not detach from ramp during rolling.

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## Homework Equations

## The Attempt at a Solution

a)

I wanted to use the principle of conservation of energy and came up with equation like this:

[itex]mv^{2}/2=2mv_{0}^{2}/2 + mgh[/itex]

Where v is initial speed of cart (what I need to find knowing only m,h and g) and [itex]v_{0}[/itex] is speed of ramp and cart on it after the cart finish its movment in relation to ramp.

I know I need a second equation here but I can't find it. I was trying to find this equation using principle of conservation of momentum but Im not sure wheter the momentum is same on the beginning and at the end of movement.

b)

Here I need to know what is the speed of the ramp after the cart 'jumps' of it, then I know how to calculate the distance when I know it. But still I need help with finding out the speed of the ramp.

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