A pendulum swings through an angle of 22 degrees each second. If the pendulum is 30 inches long, how far does its tip move each second?

We need to find the arclength of a central angle of 22°

let's use a ratio
arc/(2π(30)) = 22/360
arc = 22(60π)/360 = appr 11.5 inches/sec

To find how far the tip of the pendulum moves each second, we can use the formula for arc length. The arc length of a circle is given by the formula:

Arc length = radius x angle

In this case, the radius of the pendulum is 30 inches and the angle it swings through each second is 22 degrees.

Converting the angle from degrees to radians, we have:

Angle in radians = (22 degrees) x (π/180 radians/degree)

≈ 0.383972 radians

Now we can calculate the arc length using the formula:

Arc length = (30 inches) x (0.383972 radians)

≈ 11.51916 inches

Therefore, the tip of the pendulum moves approximately 11.52 inches each second.

To determine how far the tip of the pendulum moves each second, we need to find the length of the arc it traces out.

The length of an arc, denoted as "s", can be calculated using the formula:

s = l * θ

Where:
s is the length of the arc
l is the length of the pendulum
θ is the angle in radians

However, the given angle is in degrees, so we need to convert it to radians before using the formula.

To convert an angle from degrees to radians, we use the formula:

θ_radians = θ * (π / 180)

Where:
θ_radians is the angle in radians
θ is the given angle in degrees

Given that the angle is 22 degrees:

θ_radians = 22 * (π / 180)

Now, we can substitute the values into the formula for the length of the arc:

s = 30 * (22 * (π / 180))

Calculating this expression will give us the length of the arc that the tip of the pendulum moves.