Question

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of π . ​​30 min

Accepted Answer

Identify the radius of the circular path traveled by the tip of the minute hand. Since the tip is 3 inches from the center, the radius $$r is 3 $$inches. Recall that the distance traveled by a point moving along a circular path is the length of the arc it covers. The formula for arc length $$s is$$ $$s = r 	heta$$, where $$	heta is $$the central angle in radians. Determine the fraction of the full circle the minute hand moves in 30 minutes. Since the minute hand completes one full rotation (360 degrees or $$2\pi$$ radians) in 60 minutes, in 30 minutes it moves half the circle, so $$	heta = \pi$$ radians. Calculate the arc length using the formula $$s = r 	heta. $$Substitute $$r = 3$$ inches and $$	heta = \pi$$ radians to express the distance traveled as a multiple of $$\pi. $$Write the final expression for the distance traveled by the tip of the minute hand in 30 minutes as $$3\pi$$ inches, leaving the answer in terms of $$\pi as $$requested.

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of π . 30 min

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Key Concepts

Arc Length Formula

Conversion Between Degrees and Radians

Minute Hand Movement and Angular Displacement