Conservation of Energy in Gravity

AI Thread Summary
The discussion revolves around calculating the final speed of a boy falling from a roller coaster using conservation of energy principles. For an initial speed of 0, the final speed is determined using the formula v = √(2gh), resulting in 19.8 m/s. When starting with an initial speed of 5 m/s, the equation v² = u² + 2gh is applied, yielding a final speed of 20.4 m/s. The user expresses confusion over the calculations and seeks clarification on the process. The thread highlights the importance of understanding energy conservation in gravitational contexts.
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Homework Statement


A boy at the top of a roller coaster falls through a vertical distance of 20m. What is the final speed of the boy if:
a) His initial speed was 0
b) His initial speed was 5 ms-1


Homework Equations


GPE at top = KE at bottom
mgh = 1/2mv^2
gh = 1/2v^2
v = √2gh

if the initial velocity (u) was not equal to zero, the maths becomes slightly different

initial total energy = final total energy
1/2mu^2 + mgh = 1/2mv^2

therefore...

v^2 = u^2 + 2gh


The Attempt at a Solution



a) 2x9.8x20 = 392

b) 5^2 + 2x9.8x20 = 417


The answers are:
a) 19.8 ms-1
b) 20.4 ms-1
What on Earth am I doing wrong... what can I do... or what? D: I just don't understand!
 
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If v2=392 m2/s2, what is v?
 
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Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

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Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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