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The vector diagram (net force on the dog down the slide) is drawn
wrong. If you sum up the vectors shown (friction, normal force,
gravity),
Worse is the last sentence of the paragraph above the vector diagram:
"To find out how fast the dog will slide, we need one other piece of
information, his mass."
This is an abjectly incorrect statement. The acceleration down the
slide is g(sin(theta) - mu*cos(theta)). Not only is mass not needed,
but the other piece of information needed is mu (and of course theta).