Speed and distance based problem: Find the final speed of the rolling hoop

What is the final speed of the hoop rolling down a 4.75 m high hill without slipping? The final speed of the hoop can be calculated using the conservation of energy principle.

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.

Conservation of Energy Equation:

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.

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