



 
Hi William. I've drawn the scene, forces and force components below.
First, I hope you can recognize that the angle θ for the ramp is the same as the angle θ between the force due to gravity (F_{g }) and its component perpendicular to the ramp (F_{y }). This is due to similar triangles. Now, you want the coefficient of kinetic friction and that is μ in the equation F_{f } = μ F_{N}, where F_{f } is the force of friction and F_{N} is the normal force. Thus we have:
You know that the magnitude of the normal force F_{N } is the same as the magnitude of the force F_{y } (otherwise the couch would be sinking into the ramp or levitating!) But right triangle trigonometry tells us that F_{y } = F_{g }cos θ. So:
I've transcribed the frictional force from the top of the diagram to the bottom so you can see how it has to add up. The resultant force (giving rise to the acceleration of the couch) is F_{R}. This is a result of the component of the gravitational force that is parallel to the ramp (F_{x }) and the frictional force that opposes it (F_{f }). So (using magnitudes only), F_{f } = F_{x }  F_{R }. This means:
Again using standard right triangle geometry, we know that F_{x } = F_{g } sin θ, so:
By Newton's Law, the resultant force F_{R } = ma_{R }, where a_{R } is the resultant acceleration. Thus,
And lastly, F_{g } is simply mg, so the mass cancels out and our final equation is:
So from here, you have all the values you need. Note that the question says the resultant acceleration is 0.70 meters per second [sic]. Meters per second isn't an acceleration, so something is wrong with the question. My guess is this is a typo and it should say 0.70 meters per second^{2 }. Hope this helps,  


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