Velocity of object sliding down incline, given gravity and the incline's height

AI Thread Summary
A cart slides down a 159m high incline with an initial speed of 0m/s and gravity at 9.8 m/s², while neglecting friction and air resistance. The discussion centers on determining the cart's speed at the bottom of the incline without knowing the incline's angle or length. One participant suggests using the conservation of energy principle, stating that the initial and final energy states are equal, which simplifies the problem since mass cancels out. Another participant notes that while classical motion equations could be used, the angle of the incline is not necessary for the energy conservation approach. The conversation emphasizes understanding the application of energy conservation in solving the problem.
jstep
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Homework Statement



a cart slides down an iced incline that is 159m high.

initial speed is 0m/s

acceleration of gravity is 9.8 m/s^2

neglect friction, air resistance

determine carts speed at the bottom of the hill

Homework Equations



v = u + at, but no time is mentioned

v^2 = u^2 + 2ah, if i treat it like freefall

The Attempt at a Solution



i don't hardly know where to start with this one, my first instinct was to break the two-dimensional motion into component vectors. but then i realized i don't have the length of the incline or even the angle of the incline, only the height.

i don't have any notion of time either, so i can't use v = u + at

i could treat it like freefall and use v^2 = u^2 + 2ah

v = sqrt(u^2 + 2ah), u = 0

v = sqrt((2)(9.8)(159))

v = 55.82 m/s

but i don't believe i can treat it like freefall, because aren't you supposed to be able to break up two-dimensional velocity into vectors that are completely independent of each other? and i believe the question is asking for the v in the x direction.

i'm not asking for an answer, i need to understand how to do it myself. but i don't think I'm approaching this problem with the right process. I think i just need a nudge in the right direction.

Thank you.
 
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jstep said:

Homework Statement


v = u + at, but no time is mentioned
Thats why we love conservation laws. :smile:

What is constans during ride down?

regards
 
the only thing that is constant is acceleration in the y-direction, acceleration in the x-direction is increasing. are you speaking of conservation of energy? I don't understand how that applies to this scenario... I don't even have the object's mass.
 
jstep said:
the only thing that is constant is acceleration in the y-direction, acceleration in the x-direction is increasing. are you speaking of conservation of energy? I don't understand how that applies to this scenario... I don't even have the object's mass.
Energy is constans and of course I suggest use energy conservation law. To apply this you should assume, that you are know mass - it will be reduced.

The beauty of the conservation of energy law lies in the fact that no matter what happens in the meantime. No matter distance, time etc. You know energy at the start time, and at the end. They are equal. Thats all.

regards
Bartek
ps
of course you can solve this using classical movement equations. You have to assumed that you know the angle of hill, then find distance and qravity force component parallel to hill. No matter, that you in fact don't know that angle - it will be reduced.
 
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