$21.$ Rain starts falling vertically down into a cart with frictionless wheels which is initially moving at a constant velocity on a horizontal surface. The rain drops come to rest with respect to the cart after striking it$,$ and rain water accumulates in the cart. Select all of the following statements that must be true about this situation.$(1)$ The cart will continue to move at a constant velocity because the rain is falling vertically while the cart is moving horizontally.$(2)$ The cart will continue to move at a constant velocity because the total mechanical energy of the cart$-$rain system is conserved.$(3$ The cart will slow down because the horizontal momentum of the cart$-$rain system is conserved.ramm$($a$)(1)$ only$($b$)$only$($c$)(3)$ only$($d$)(1)$ and $(2)$ only$($e$)$ None of the above