Answer:
V' = 0.84 m/s
Explanation:
given,
Linear speed of the ball, v = 2.85 m/s
rise of the ball, h = 0.53 m
Linear speed of the ball, v' = ?
rotation kinetic energy of the ball

I of the moment of inertia of the sphere

v = R ω
using conservation of energy


Applying conservation of energy
Initial Linear KE + Initial roational KE = Final Linear KE + Final roational KE + Potential energy



V'² = 0.7025
V' = 0.84 m/s
the linear speed of the ball at the top of ramp is equal to 0.84 m/s

The net force acting on the block is ~


So, the Answer in the boxes will be ~

Answer:
a = v^2/r centripetal acceleration
v = (a * r)^1/2 = (42 * .23)^1/2 = 3.1 m/s