Solving a Ski Slope: Length & Time for Descent

AI Thread Summary
The discussion focuses on a physics problem involving a skier descending a 10-degree incline from an initial speed of 3 m/s to a final speed of 15 m/s. The key challenge is determining the acceleration due to gravity's component along the incline. The correct approach involves using the formula for gravitational force parallel to the incline, which is mgsin(theta), to find the acceleration. The participant initially miscalculated the acceleration, incorrectly deriving it as 56.4 instead of using the appropriate equation of a = gsin(10). Clarification on the correct method is sought due to an upcoming exam.
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Homework Statement


A skier is gliding along at 3m/s on horizontal frictionless snow. He suddenly starts down a 10 degree incline. His speed at the bottom is 15 m/s.
a) what is the length of the incline?
b) how long does it take for him to reach the bottom?
we know:
Vo=3m/s
Vf=15m/s
t=?
x=?
a=?

Homework Equations


V^2=Vo^2 +2ax



The Attempt at a Solution


i need help to find what the a is...and why it is that.
 
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the only force acting on the skier is gravity but since the skier is going down a 10 degree incline gravity is giving him some acceleration but not 100% of it's full foce.

draw the Free Body Diagram and split up gravity into it's components where the acceleration will be parallel to the incline.
 
okay from my freebody diagram i get sin(10)=9.8/a
a=56.4
and that is wrong...if anyone could explain to me how to do it properly please...id greatly appreciate it because i have my exam very soon.
 
it should be 9.8*sin(10). the force acting parallel to the inclined plane is mgsin(theta).
 
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