Final answer:
To calculate the length of arc a pendulum tip moves each second, convert the 20 degrees to radians and multiply by the length of the pendulum. The arc length is 8π/9 inches.
Step-by-step explanation:
A pendulum moves at an angle of 20 degrees each second, and we are asked to calculate how far the tip moves each second, given the pendulum is 8 inches long. To find the length of the arc that the pendulum sweeps out, we can use the formula for the length of an arc on a circle, which is θr, where θ is the angle in radians and r is the radius of the circle (the length of the pendulum).
First, we need to convert the angle from degrees to radians. There are π radians in 180 degrees, so 20 degrees is equal to (20/180)π radians. Then, we multiply this angle in radians by the length of the pendulum to find the length of the arc:
• Convert 20 degrees to radians: 20° × (π/180) = π/9 radians
• Calculate the arc length: length = radius × angle in radians = 8" × (π/9) = 8π/9 inches
This gives us the length of the arc that the pendulum tip moves each second, which can simply be calculated numerically if required.