A 1 kg object starts 3 meters from the ground on a 24 degree incline with a friction coefficient of 0.12. When it hits the ground, it collides and sticks to a 8 kg object. The coefficient friction on the horizontal surface is 0.24 How far do the objects travel away from the incline?
Use a conservation of energy method to get the velocity of the 1 kg object at the base of the incline.
(potential energy loss) = (work done against friction) + (kinetic energy at bottom)
Once you have that velocity (V), use conservation of momentum to get the velocity V' of the two masses stuck together, before they start to slide. It looks like V' will be V/9. Do you see why?
Then use conservation of energy again (with friction work) to get the distance that the masses slide horizontally.
Show your work if you need further help.