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A ski-jumper starts from rest 50 m above the base of a ski jump, accelerating down the ramp to the bottom where she is launched horizontally into the air. The ski jump is on top of a hill such that the ground slopes steeply downwards beyond the jump, allowing the ski-jumper to fall a great distance before landing.

Assuming no friction or air resistance act on the ski-jumper, and assuming her time of flight is 2 seconds, what are the coordinates of her landing position? Define the position (0, 0) as being the end of the ski jump where the skier is launched into the air, with the skier initially moving in the $+x$-direction and the $+y$-direction being defined as vertically upward.


$(63\space m, -20\space m)$


$(43\space m, -20\space m)$


$(31\space m, 43\space m)$


$(20\space m, 43\space m)$

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