Clock Hand Angle Calculation
This problem requires calculating the angle covered by the clock's minute hand based on the angle covered by the second hand in a specific time frame.
Calculating Time from Second Hand Movement
First, determine the time it takes for the second hand to cover 3240°.
- Speed of the second hand: The second hand moves 360° in 60 seconds, which is \(\frac{360^\circ}{60 \text{ s}} = 6^\circ\) per second.
- Time taken: \(T = \frac{\text{Total Angle}}{\text{Speed}} = \frac{3240^\circ}{6^\circ/\text{s}} = 540 \text{ seconds}\).
Calculating Minute Hand Movement
Next, find the angle the minute hand covers in 540 seconds.
- Convert time to minutes: 540 seconds is equal to \(\frac{540}{60} = 9\) minutes.
- Speed of the minute hand: The minute hand moves 360° in 60 minutes, which is \(\frac{360^\circ}{60 \text{ min}} = 6^\circ\) per minute.
- Angle covered by the minute hand: Angle = Speed × Time = \(6^\circ/\text{min} \times 9 \text{ min} = 54^\circ\).
Therefore, the minute hand covers 54° in the same time the second hand covers 3240°.
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