A clock has an hour hand of length 2.4 cm and a minute hand of length 3.8 cm. (a) Calculate the position and velocity of the hou

Question

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r hand at noon. (b) Calculate the position and velocity of the minute hand at 12:15.

1 answer:

Ostrovityanka [942] · Answer 1 · 2026-03-04T13:07:34+03:00

Answer:

At 12:00, the hour hand is positioned at 0 degrees, with its tip moving at an estimated 1.26 cm/hour.
At 12:15, the minute hand is at 90 degrees, traveling at roughly 23.88 cm/hour.

Explanation:

The position is established by an angle, which begins at the 12:00 point and extends clockwise.

At noon, the hour hand is at the 12:00 position, thus its position is 0 degrees; it has an angular velocity of (2π)/(12 hours) = π/(6 hours). Therefore, the tip moves at a linear velocity of (2.4 cm) * π/(6 hours) ≅ 1.26 cm/hour.

At 12:15, the minute hand is at the 3 o'clock position, giving it a position of 90 degrees or π/2; its angular velocity is (2π)/(1 hour) = 2π/hour. Thus, the tip moves at a linear velocity of (3.8 cm) * 2π/hour ≅ 23.88 cm/hour.