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$($p$28)$A child of mass $35$ kg sits on a wooden horse on a carousel. The wooden horse is $3\mathrm{.}3$ m from the center of the carousel, which rotates at a constant rate and completes one revolution every $5\mathrm{.}2$ s $.($a$)$ What are the magnitude and direction $($tangential in direction of velocity, tangential in the opposite direction of the velocity, radial outward, radial inward$)$ of $\frac{dp}{dt}$hat$(p),$ the parallel component of $(\frac{d(vec(p))}{dt}{)}_{||}$for the child? $($b$)$ What are the magnitude and direction of $p\frac{d(hat(p))}{dt},$ the perpendicular component of for the child? $($c$)$ What are the magnitude and direction of the net force acting on the child? $($d$)$ What objects in the surroundings contribute to this horizontal net force acting on the child? $($There are also vertical forces, but these cancel each other if the horse doesn't move up and down.$)$