How Long Does It Take a Skier to Descend a 22° Incline?

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SUMMARY

The discussion centers on a kinematics problem involving a skier descending a 22° incline. The skier starts with an initial speed of 2.91 m/s on a horizontal surface and reaches a final speed of 12.18 m/s at the bottom of the incline. The length of the incline has been calculated as 19.0610 m. The main query is about determining the time it takes for the skier to reach the bottom of the incline.

PREREQUISITES
  • Understanding of basic kinematics principles
  • Familiarity with the equations of motion
  • Knowledge of trigonometry related to angles and slopes
  • Ability to apply conservation of energy concepts
NEXT STEPS
  • Calculate the time taken using the kinematic equation: \( t = \frac{v_f - v_i}{a} \)
  • Explore the derivation of acceleration on an incline using \( a = g \sin(\theta) \)
  • Investigate the impact of friction on incline problems
  • Review energy conservation principles in the context of inclined planes
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Students studying physics, educators teaching kinematics, and anyone interested in solving problems related to motion on inclined planes.

dougr81
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Hi,
I am having some trouble with this simple kinematics problem. Here it is:

A skier is gliding along at 2.91 m/s on horizontal, frictionless snow. He suddenly starts down a 22° incline. His speed at the bottom is 12.18 m/s.

The first question asks for the length of the incline, which I got 19.0610 m.

The second question asks how long it takes to reach the bottom. Can anyone help me set this up?

Thanks,
Doug
 
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