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Conservation of Energy on a frictionless incline

  • Thread starter Ly444999
  • Start date
1. Homework Statement
A 259 g textbook slides up a 22.1° incline that is 2.55 m long. Using conservation of energy and assuming the incline is frictionless, what minimum initial speed is needed to accomplish this?
mass = 0.259 kg
Θ = 22.1°
length of incline = 2.55 m
2. Homework Equations
KE = (1/2)*mv2
PE = mgh

3. The Attempt at a Solution
I solved for height of the incline/ramp using trigonometry where the height is opposite to the angle and the length of the ramp is the hypotenuse:
h = 2.55*sin(21.5°) = 0.934

Since the incline is frictionless the kinetic energy at the beginning is equal to the potential energy of when the textbook reaches the top of the ramp:
KE = PE
(1/2)*mv2 = mgh
Isolating for the velocity, the masses cancel out
v = √2gh
v = √(2*9.8*0.934)
= 4.27 m/s

So I got 4.27 m/s as initial velocity but it doesn't match with any of the answers which are either 4.34 m/s, 7.07 m/s, 3.07 m/s or 6.80 m/s.

So I was wondering what I did wrong. Was the velocity I was solving for not initial velocity or was the approach completely wrong? or Did I just make some miscalculations that made it not equal to the first answer?
 
Notice anything?
****, ok I'm very unintelligent, for some reason in my calculations I'm using 21.5 as my degrees I don't know why, thank you for pointing out my obvious mistake though lol.
Edit: I got right answer thank you lol.
 

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