A block is projected up a frictionless inclined plane with a speed v o. The angle of incline is θ. (a) How far up the plane does it go? (b) How long does it take to get there? (c) What is its speed when it gets back to the bottom?

Question

A block is projected up a frictionless inclined plane with a speed v o.  The angle of incline is θ.  (a) How far up the plane does it go?  (b) How long does it take to get there?  (c) What is its speed when it gets back to the bottom?

anonymous · Answer

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(a) Acc. to Conservation of Energy:
mgh=1/2mVo^2
So, h=(Vo^2)/2g
so x=hcosec(-)={(Vo^2)/2g}Coesec(-)

(b) 0=VoSin(-) - gt   (from v=u + at)
so, t=VoSin(-)/g

(c) speed at bottom = Vo (Conservation of mechanical energy)