Solving for Time Taken to Slide Down Roof

[Vanessa23]

Homework Statement

a ball started at a height of 12.5 meters and rolled to the edge of a roof which is at 7 meters. Using a^2+b^2=c^2 we know it rolled a distance of 8.14 meters on the roof because it rolled a horizontal distance of 6m and a vertical distance of 5.5m. Find the time it rolled down the roof. The roof makes a 40deg angle with the horizontal and coeff of friction is .388.

Homework Equations

Potential E=KE+Ffriction
mg*distance*sin(theta)=.5mv^2+(coeff of friction)*mgcos(theta)*distance down roof
acceleration=g*sin(theta)-g*(coeff. of friction)*cos(theta)
V=Vo+at

The Attempt at a Solution

8.14*g*sin(40)=.5v^2+.388*g*cos(40)*(8.14)
v=9.84m/s

a=g*sin40)-g*.388cos(40)
a=3.39m/s^2

9.84=3.39t
t=2.90 seconds

 

[saket]

a ball started at a height of 12.5 meters and rolled to the edge of a roof ...
... we know it rolled a distance of 8.14 meters on the roof because it rolled a horizontal distance of 6m and a vertical distance of 5.5m. Find the time it rolled down the roof. ...

What you have solved is for sliding down the roof whereas, the question has reiterated the term rolling. I think, question has been manipulated, in your own words!

The attempt is correct, method-wise, if it is sliding. So, have you written 'sliding' incorrectly?
If it is indeed 'rolling', one information is missing: information about the ball? Assuming a spherical ball (as most of them are), is it solid or hollow? Have you missed that?