In a circus performance, a large 5kg hoop of radius 3m rolls without slipping. If the hoop is given an angular speed of 3 rad/s while rolling on the horizontal and allowed to roll up a ramp inclined at 20 degrees with the horizontal, how far(measured along the incline) does the hoop roll?

My solution is as follows:

Total initial energy=0.5 * I * (angular velocity)^2

=0.5 * 45 * 3^2

=202.5

Final energy = mgh

= 5gh, where h is the vertical height

Equating the 2,

202.5=5gh

h=4.128.

Since we want to find the distance along the slope, d, d=h/sin20 =

__12.1m__

This is the ans I got, but it seems that the back of the textbook ans is

**24m**. Is the textbook ans correct or wrong?