A $50\mathrm{.}0-$kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of $24\mathrm{.}0$ m$.$

$($a$)$ What is the centripetal acceleration of the child?

magnitude $$ m$/$s$2$direction $---$Select$---$toward the center of the path$$away from the center of the path$$tangent to the path$$The magnitude is zero.

$($b$)$ What force $($magnitude and direction$)$ does the seat exert on the child at the lowest point of the ride?

magnitude $$ Ndirection $---$Select$---$up toward the center$$down away from the center$$tangent to the left$$tangent to the right$$The magnitude is zero.

$($c$)$ What force does the seat exert on the child at the highest point of the ride?

magnitude $$ Ndirection $---$Select$---$up away from the center$$down toward the center$$tangent to the left$$tangent to the right$$The magnitude is zero.

$($d$)$ What force does the seat exert on the child when the child is halfway between the top and bottom? $($Assume the Ferris wheel is rotating clockwise and the child is moving upward.$)$

magnitude $$ Ndirection $$ counter$-$clockwise from the horizontal