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Assuming metric units, metre, kilogram and seconds

Best approach: draw a free body diagram and identify forces acting on the child, which are:

gravity, which can be decomposed into normal and parallel (to slide) components

N=mg(cos(theta)) [pressing on slide surface]

F=mg(sin(theta)) [pushing child downwards, also cause for acceleration]

m=mass of child (in kg)

g=acceleration due to gravity = 9.81 m/s^2

theta=angle with horizontal = 42 degrees

Similarly, kinetic friction is slowing down the child, pushing against F, and equal to

Fr=mu*N=mu*mg(cos(theta))

mu=coefficient of kinetic friction = 0.2

The net force pushing child downwards along slide is therefore

Fnet=F-Fr

=mg(sin(theta))-mu*mg(cos(theta))

=mg(sin(theta)-mu*cos(theta)) [ assuming sin(theta)> mu*cos(theta) ]

From Newton’s second law,

F=ma, or

a=F/m

=mg(sin(theta)-mu*cos(theta)) / m

= g(sin(theta)-mu*cos(theta)) [ m/s^2]

In case imperial units are used, g is approximately 32.2 feet/s^2.

and the answer will be in the same units [ft/s^2] since sin, cos and mu are pure numbers.

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