Speed and distance based problem: Find the final speed of the rolling hoop
Calculating the Final Speed:
Given the height of the hill, h = 4.75 m, we can use the conservation of energy equation to determine the final speed of the rolling hoop.
mgh = 1/2 mv^2 + 1/2 Iω^2
Where:
m = mass of the hoop
g = acceleration due to gravity
v = final velocity of the hoop
I = moment of inertia of the hoop
ω = angular velocity
By substituting the values and simplifying the equation, we can find:
v = √(gh)
v = √(9.8 * 4.75)
v = 6.822 m/s
Therefore, the final speed of the hoop rolling down a 4.75 m high hill without slipping is 6.822 m/s.