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Classical Mechanics

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Difficult

Ski-Jumper with Lift

CLMECH-UTLNN9

A ski-jumper of mass $m$ starts from rest a height $h$ above the base of a ski jump, traveling a distance $d$ 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. While on the ramp, an average frictional force $f$ acts on the ski-jumper and once in the air she experiences a lift force, $L$ (ignore all other effects of air resistance).

If the ski-jumper lands $\Delta y$ meters below the base of the jump, what is the expression for her horizontal range (relative to the end of the ski jump)?

A

$\Delta x = 2\sqrt{\cfrac{\Delta y\left (f/mg - h\right )}{L-g}}$

B

$\Delta x = \sqrt{2\left (gh - \frac{fd}{m}\right )}$

C

$\Delta x = 2\sqrt{\Delta y\left (\frac{fd}{mg} - h\right )}$

D

$\Delta x = 2\sqrt{\cfrac{\Delta y (gh - fd/m)}{L/m - g}}$