Roller coaster problem involving velocity

AI Thread Summary
A roller coaster starts at 7.0 km/h and descends a 46.0 m hill at a 43° angle, with a kinetic friction coefficient of 0.12. The calculations involve determining the frictional force and net acceleration using F=ma and kinematic equations. The initial attempt yielded an acceleration of 5.82, but the correct answer for the final speed should be 83.6 km/h. The user realized the acceleration units were incorrectly noted and confirmed they are m/s². The discussion highlights the importance of unit consistency in physics calculations.
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Homework Statement



A roller coaster reaches the top of the steepest hill with a speed of 7.0 km/h. It then descends the hill, which is at an average angle of 43° below horizontal and is 46.0 m long. What will its speed be when it reaches the bottom? Assume the coefficient of kinetic Friction is 0.12.

Homework Equations


Ff= U•Fn
F=ma
Vf ^2 - Vo^2 = 2ad

The Attempt at a Solution


Ff=U•Fn
Ff= U•mgcos(43)

F=ma
Mgsin(43) - Umgcos(43) =ma
The mass cancels out here so ,
gsin(43) - Ugcos(43) = a
5.82 = a

Vf= (square roof of>>) 2ad + vo ^2
Vf = (square roof of >> ) 2 • 5.82 • 0.046 + 7.0^2
Vf = 7.04 km/h

The answer should be 83.6 km/h
Where did I go wrong
 
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y90x said:
5.82 = a
What are the units for this acceleration?
 
TSny said:
What are the units for this acceleration?

I just realized it was m/s^2
Thank you
 
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