Find exit speed at the bottom of the ramp using kinematics only

AI Thread Summary
The discussion centers on calculating the exit speed of a skier at the bottom of a ramp using kinematics, considering the effects of friction and air resistance. The skier's initial acceleration is 90% of that on a frictionless incline, and the speed record at the bottom of a 29-degree slope is 180 km/h. The initial calculations led to an exit speed of 223.7 km/h, but this was incorrect due to not accounting for the 90% acceleration factor. The correct approach involves adjusting the acceleration to reflect the frictional loss. Ultimately, the skier's ideal speed in the absence of air resistance is lower than initially calculated.
spartan55
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Homework Statement


A professional skier's initial acceleration on fresh snow is 90% of the acceleration expected on a frictionless, inclined plane, the loss being due to friction. Due to air resistance, his acceleration slowly decreases as he picks up speed. The speed record on a mountain in Oregon is 180 kilometers per hour at the bottom of a 29.0deg slope that drops 197 m. What exit speed could a skier reach in the absence of air resistance (in km/hr)? What percentage of this ideal speed is lost to air resistance?


Homework Equations


We are only on kinematics...
(v_final)^2 = (v_initial)^2 + 2*(a_parallel)*(x_final - x_initial) , where a_parallel = g*sin(29)


The Attempt at a Solution


I used trig to solve for the length of the ramp:
l*sin29 = 197
l = 406.35 m
Then I plugged this into the above kinematics equation and solved for v_final:
(v_final)^2 = 0 + 2*g*sin(29)*(406.35 - 0)
v_final = 62.14 m/s
I converted this to km/hr:
62.14 m/1s * 1km/1000m * 3600s/1hr = 223.7 km/hr, but this isn't the correct answer. I'm not sure where I went wrong.
 
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spartan55 said:

Homework Statement


A professional skier's initial acceleration on fresh snow is 90% of the acceleration expected on a frictionless, inclined plane, the loss being due to friction. Due to air resistance, his acceleration slowly decreases as he picks up speed. The speed record on a mountain in Oregon is 180 kilometers per hour at the bottom of a 29.0deg slope that drops 197 m. What exit speed could a skier reach in the absence of air resistance (in km/hr)? What percentage of this ideal speed is lost to air resistance?


Homework Equations


We are only on kinematics...
(v_final)^2 = (v_initial)^2 + 2*(a_parallel)*(x_final - x_initial) , where a_parallel = g*sin(29)


The Attempt at a Solution


I used trig to solve for the length of the ramp:
l*sin29 = 197
l = 406.35 m
Then I plugged this into the above kinematics equation and solved for v_final:
(v_final)^2 = 0 + 2*g*sin(29)*(406.35 - 0)
v_final = 62.14 m/s
I converted this to km/hr:
62.14 m/1s * 1km/1000m * 3600s/1hr = 223.7 km/hr, but this isn't the correct answer. I'm not sure where I went wrong.
Look at the phrase in red, especially the 90%.
 
Ahh yes that is what I forgot. Thanks Sammy!
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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