A frictionless plane is $10\mathrm{.}0$ m long and inclined at $31\mathrm{.}5.$ A sled starts at the bottom with an initial speed of $5\mathrm{.}25$ m$/$s up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed vi$.$ Both sleds reach the bottom of the incline at the same moment.

$($a$)$ Determine the distance that the first sled traveled up the incline.

$($b$)$ Determine the initial speed of the second sled.