Aregulation basketball has a 47 cm diameter and may be approximated as a thin spherical shell.
how long will it take a basketball starting
from rest to roll without slipping 3.5 m down
an incline that makes an angle of 80.6◦ with
the horizontal? the acceleration of gravity is 9.81m/s^2
answer in units of s.

1.1 s

Explanation:

The initial ball’s height is

From the law of conservation of energy, the potential energy converts to kinetic energy

Where m is mass, g is acceleration due to gravity, h is height, v is the velocity

Here, the potential energy converts to potential energy and rotation energy

Moment of inertia of the ball, and making r the subject then substituting it back to the equation of rotation energy we obtain rotational energy as

From kinematics

Since then and