QUESTION 13 How many degrees will the second-hand move, in the same time in which the...
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How many degrees will the second-hand move, in the same time in which the minute hand moves 34°?
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Answer: A. 2040°
The second-hand completes 360° in 60 seconds, while the minute-hand completes 360° in 60 minutes (3600 seconds). Therefore, the second-hand moves 60 times faster than the minute-hand. When the minute-hand moves 34°, the second-hand moves 34° × 60 = 2040°.
Step-by-step Derivation:
Step 1: Determine angular velocities.
- Minute-hand: 360° per 60 minutes = 6° per minute
- Second-hand: 360° per 60 seconds = 6° per second
Step 2: Find the time taken for minute-hand to move 34°.
- Time = 34° ÷ 6° per minute = 34/6 minutes = 5.667 minutes = 340 seconds
Step 3: Calculate second-hand movement in 340 seconds.
- Second-hand moves 6° per second
- In 340 seconds: 340 × 6° = 2040°
Alternatively, using the speed ratio:
- Speed ratio (second-hand : minute-hand) = 60 : 1
- When minute-hand moves 34°, second-hand moves 34° × 60 = 2040°