Conservation of rotational energy

[vu10758]

A cylindrical can of paint with (I = .5MR^2) starts from rest and rolls down a roof as shown in the link
http://viewmorepics.myspace.com/index.cfm?fuseaction=viewImage&friendID=128765607&imageID=1424481748

Determine how far the can lands from the edge of the house.
This is my work, but I am not getting the correct answer. Please tell me where I messed up. The correct answer is 6.18m

mgH = (1/2)MV_cm^2 (1+B)
gH = (1/2)V_cm^2 (1+B)
3g = (1/2)V_cm^2(1+.5)
3g = (3/4)v_cm^2
4g = v_cm^2
v = 2SQRT(g)

Now, I know that x = x_0 + v_o*cos(theta)*t

x = 2SQRT(g)*cos(30)*t

To solve for t, I used y

y = 10 - 2SQRT(g)*sin(30)*t - (1/2)gt^2
0 = 20 - 4SQRT(g)*sin(30)*t - gt^2
0 = gt^2 + 2SQRT(g)*t - 20

t = 2SQRT(g) +/- SQRT[4g-4(g)(-20)]/2g
t = 7.72 seconds or 4.79

x = 2SQRT(g)*cos(30)*7.72
x = 41.8

x = 2SQRt(g)*cos(30)*4.79
x = 26.0

The correct answer is 6.18. My answer is too far off, but I don't know where I went wrong.

 

[Hootenanny]

I'm not sure what your initial equation is meant to represent, but note that total energy must be conserved. i.e,

gravitational potential = rotational kinetic energy + linear kinetic energy

 

[kyle8921]

Your calculation for the initial velocity (v) is correct, but your calculation for the time (t) is incorrect. The correct formula for finding the time is t = (-v/g) + (2H/g). Plugging in the values, we get t = (-2SQRT(g)/g) + (2(10)/g) = 2.22 seconds.

Now, we can use this value for t in the equation x = x_0 + v_0*cos(theta)*t to find the distance (x) the can lands from the edge of the house. Plugging in the values, we get x = 0 + (2SQRT(g)*cos(30)*2.22) = 6.18m, which matches the correct answer.

In summary, your calculation for the initial velocity was correct, but you made a mistake in calculating the time. Make sure to double check your equations and units when solving problems involving conservation of rotational energy.