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°?
Show answer & explanation
The second-hand completes 360° in 60 seconds, while the minute-hand completes 360° in 3600 seconds (60 minutes). 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 the angular velocities.
- Minute-hand: 360° in 3600 seconds = 0.1°/second
- Second-hand: 360° in 60 seconds = 6°/second
Step 2: Calculate the time taken for minute-hand to move 34°.
- Time = 34° / 0.1°/second = 340 seconds
Step 3: Calculate the distance the second-hand moves in 340 seconds.
- Distance = 6°/second × 340 seconds = 2040°
Alternatively, note that the second-hand moves 60 times faster than the minute-hand (since it completes one full rotation in 1/60th the time). Thus: 34° × 60 = 2040°