A basketball rolls without slipping (starting from rest) down a ramp. If the ramp is sloped by an angle of 4 degrees above the horizontal and the ball rolls for a distance of 60 m along the ramp, what is its speed after rolling this far? The moment of inertia of a basketball is 1.

11.7 m/s

Explanation:

To find its speed, we first find the acceleration of the center of mass of a rolling object is given by

a = gsinθ / (1 + I/MR²) where θ = angle of slope = 4, I = moment of inertia of basketball = 2/3MR²

a = 9.8 m/s²sin4 (1 + 2/3MR²/MR²)

= 9.8 m/s²sin4 (1 + 2/3)

= 9.8 m/s²sin4 * (5/3)

= 1.14 m/s²

To find its speed v after rolling for 60 m, we use

v² = u² + 2as where u = initial speed = 0 (since it starts from rest), s = 60 m

v = √ (u² + 2as) = √ (0² + 2 * 1.14 m/s * 60 m) = √136.8 = 11.7 m/s