Physics. The speed of a child riding a merry-go-round at a...

Physics. The speed of a child riding a merry-go-round at a carnival is given by the equation $v=\sqrt{12 r},$ where $v$ is the speed in feet per second and $r$ is the distance in feet from the center of the merry-go-round to the rider. If a child is moving at $15 \mathrm{ft} / \mathrm{s}$ how far is the child from the center of the merry-go-round?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Algebraic Equation Manipulation

This concept involves using arithmetic operations to rearrange an equation and isolate the unknown variable. In many physics problems, especially those involving formulas, algebraic manipulation is essential for expressing one quantity in terms of others and solving for its numerical value.

Radical Equations

Radical equations include variables under a square root or other roots. Solving these equations typically requires isolating the radical expression and then eliminating it by raising both sides of the equation to an appropriate power, all while being cautious of potential extraneous solutions.

Circular Motion

In circular motion, quantities such as the tangential speed and the radial distance from the center are fundamentally linked. This concept explains how a particle moving in a circle possesses a speed that is dependent on its distance from the axis of rotation, and it is key in analyzing motions in systems like merry-go-rounds and other rotational contexts.

Transcript

Please give Ace some feedback