At the State Fair you see people trying to win a prize at a game booth. They are

Question

At the State Fair you see people trying to win a prize at a game booth. They are sliding a metal disk shaped like a puck up a wooden ramp so that it stops in a marked zone near the top of the ramp before sliding back down. You estimate that you can slide the 'puck' at v=4 m/s , but would that win the game? Find the distance d that would reach. The two boundaries of the zone appear to be at 3 and 3.2 meters from the bottom of the ramp where you release the 'puck'. The ramp appears to be inclined at 37° from the horizontal. You happen to remember that between steel and wood, the coefficients of static and kinetic friction are 0.1 and 0.08 respectively. The weight of the 'puck' is about W=12 N .

The answer is not .306 or .307.

Help a brother out.

Explanation / Answer

Let the x-axis & y-axis be shifted so that the x-axis aligns with the wooden ramp:
Wx = component of weight parallel and down ramp = 12(sin 37°) = 7.22 N
Wy = component of weight normal to the ramp = 12(cos 37°) = 9.584 N
kinetic friction force which acts down ramp on upward moving puck = (0.08)(9.584) = 0.76672 N
size of puck's deceleration down ramp = a = Fnet/m = (7.22 + 0.76672 )/(12/9.8) = 6.5225 m/s²
initial v of puck = 4 m/s
time for puck to be stopped {before falling back down ramp} = t = v/a = 4/6.5225 = 0.61326 s
distance puck travels up wooden ramp = 1/2at² = (0.5)(6.5225)(0.61326)² = 1.2265 m ANS

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