Question

a particle travels in a circle around a fixed point at 16 revolutions per minute. the linear velocity of the particle is 240\pi inches per minute. what is the distance, in inches, between the particle and the fixed point?
3.75
7.5
15
30

Explanation:

Step1: Find the circumference per revolution

The particle makes 16 revolutions per minute and has a linear - velocity of 240π inches per minute. Let \(C\) be the circumference of the circle. We know that linear velocity \(v = 16C\). So, \(C=\frac{v}{16}\). Substituting \(v = 240\pi\) inches per minute, we get \(C=\frac{240\pi}{16}=15\pi\) inches.

Step2: Use the circumference formula to find the radius

The formula for the circumference of a circle is \(C = 2\pi r\), where \(r\) is the radius (the distance between the particle and the fixed - point). If \(C = 15\pi\), then \(15\pi=2\pi r\). Solving for \(r\), we divide both sides of the equation by \(2\pi\). So, \(r=\frac{15\pi}{2\pi}=7.5\) inches.

Answer:

7.5