108. A particle is projected up along a rough plane of inclination 45° with the horizontal. If the coefficient of friction is 0.5, the retardation is (g = acceleration due to gravity)
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Explanation:
Equating forces along X and Y axes,
where mgsinθ is the parallel component of weight and mgcosθ is the normal component
N=mgcosθ
Also,
F=mgsinθ+μ
k
mgcosθ
∴a=gsinθ+μ
k
gcosθ
∴a=g(sin45
o
+0.5cos45
o
)
∴a=
2
2
3g
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