suppose his at the bottom in case of frictional -less = v
take the length of the inclined plane = d
force on child = mg*sinθ
a = mg*sinθ /m =g*sinθ = 9.8*sin20 = 3.35 m/s2
accleration without friction = 3.35 m/s2
speed at bottom
v^2 = 0 +2*a*d
v^2 = 2*3.35*d ....i
case of friction
F =mgsinθ -μmg*cosθ
a = F/m = gsinθ -μg*cosθ
speed at bottom
(v/2)^2 = 0 +2*(gsinθ -μg*cosθ ) *d .... ii
from i and ii divide them
v^2 / ( v^2/4 ) = 2*3.35*d / ( 2*(gsinθ -μg*cosθ ) *d )
4 =3.35/ gsinθ -μg*cosθ
4 = 3.35 / ( 9.8*sin20 -μ*9.8*cos20)
from here μ≈0.273026 answer
acceleration on with friction
= gsinθ -μg*cosθ
= 9.8*sin20- 0.273026*9.8*cos20 =
=0.837504 m/s2
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