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

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SUMMARY

The discussion centers on calculating the exit speed of a professional skier at the bottom of a ramp using kinematics. The skier's acceleration is 90% of that on a frictionless inclined plane, with air resistance affecting the final speed. The calculations reveal that the ideal exit speed, without air resistance, is 223.7 km/hr, but the actual speed recorded is 180 km/hr. The discrepancy indicates that approximately 19.4% of the ideal speed is lost due to air resistance.

PREREQUISITES
  • Understanding of kinematics equations, specifically the equation (v_final)^2 = (v_initial)^2 + 2*(a_parallel)*(x_final - x_initial)
  • Knowledge of trigonometric functions, particularly sine for angle calculations
  • Familiarity with gravitational acceleration (g) and its application in inclined plane problems
  • Ability to convert units, specifically from meters per second to kilometers per hour
NEXT STEPS
  • Study the effects of friction on inclined planes in physics
  • Learn about air resistance and its impact on motion in sports physics
  • Explore advanced kinematics problems involving multiple forces
  • Investigate the principles of energy conservation in downhill skiing scenarios
USEFUL FOR

Students studying physics, particularly those focusing on kinematics, as well as athletes and coaches interested in optimizing performance in skiing by understanding the effects of friction and air resistance.

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!
 

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