What is the relationship between ramp height and final velocity of a marble?

AI Thread Summary
The discussion centers on the relationship between ramp height and the final velocity of a marble. A marble released from a 10cm ramp achieves a final velocity of 1.4 m/s, prompting the question of its velocity from a 20cm ramp. The relevant equation used is the conservation of energy, equating gravitational potential energy to kinetic energy. The initial calculations suggested a final velocity of 2 m/s for the 20cm ramp, but there was uncertainty about its accuracy. Ultimately, the poster resolved the confusion and found the correct relationship between height and velocity.
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Homework Statement


A marble is released from a 10cm ramp. Its final velocity is 1.4 m/s. If it is released from a 20cm ramp, twice the height, what will its final velocity be?

Homework Equations


E = mgy + mv^2/2
mgy = mv^2/2 (Like initial gravitational potential energy will equal final kinetic energy? Does that make sense?)

The Attempt at a Solution


I tried to use mgy = mv^2/2, where I get 2gy = v^2. For g, our physics teacher has us use 10 m/s^2, and if the height is 20cm, then (2*.2m*10m/s^2) = v^2, 400 = v^2, v = 2m/s, but I don't think that is right.

I asked my teacher for help, and he said to think about the relationship between the height and the velocity (which I think has to do with square roots, but other than that, I am lost).
 
Last edited:
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Never mind, I figured it out! :)
 

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