Question

A pendulum swings through an angle of 20° each second. if the pendulum is 40 inches long, how far does its tip move each second? round answers to two decimal places.

Answer 1

The tip of the pendulum moves approximately 2.22 inches each second.

Step-by-step explanation:

The distance that the tip of the pendulum moves each second can be calculated using the formula for the arc length of a sector of a circle. The formula is given by:

distance = (angle/360) x 2π x radius

In this case, the angle is 20°, the radius is 40 inches, and we need to convert the angle to radians. So the calculation becomes:

distance = (20/360) x 2π x 40 ≈ 2.22 inches

Therefore, the tip of the pendulum moves approximately 2.22 inches each second.

Answer 2

The tip of a 40-inch long pendulum swinging through an angle of 20° each second moves approximately 13.96 inches each second, after converting the angle to radians and using the formula for arc length.

Step-by-step explanation:

To calculate how far the tip of the pendulum moves each second, we can use the formula for the arc length (S), which is S = r\(\theta), where r is the radius (or length of the pendulum) and \(\theta is the angle in radians. First, we need to convert the angle from degrees to radians (radians = degrees \(\times \frac{\pi}{180})). Next, we plug in the values: r = 40 inches and \(\theta = 20\degree \times \frac{\pi}{180} = \frac{\pi}{9} radians).

The arc length S is therefore calculated as follows:

S = 40 \times \frac{\pi}{9}
= 40 inches \times 0.34907...
\approx 13.96 inches.

So, the tip of the pendulum moves approximately 13.96 inches each second.