At exactly 10:10 AM, the hour hand of a standard analog clock is mechanically locked in it… — State PSC Exam

At exactly 10:10 AM, the hour hand of a standard analog clock is mechanically locked in its precise current position. The minute hand is then manually rotated forward (clockwise) by exactly $210^{\circ}$ . Calculate the new angle (in degrees) formed between the hour and minute hands after this adjustment. Provide the smaller of the two possible angles.

Cevap: 35 degrees

Cevap

The smaller angle between the hands after the adjustment is 35 degrees.

The correct calculation properly tracks the absolute angular positions from the 12 o'clock reference, correctly adding the

5^{\circ}

proportional movement of the hour hand before finding the difference against the shifted minute hand.

Adım Adım Çözüm

Find the initial position of the minute hand at 10:10 AM relative to the 12 o'clock mark.

The minute hand is at the 10-minute mark. Since each minute is

6^{\circ}

, its position is

10 \times 6^{\circ} = 60^{\circ}

Establishing the starting angle of the minute hand is required before applying the rotation.

Find the exact initial position of the hour hand at 10:10 AM.

The 10 o'clock mark is at

10 \times 30^{\circ} = 300^{\circ}

. In 10 minutes, the hour hand drifts

10 \times 0.5^{\circ} = 5^{\circ}

. The exact position is

300^{\circ} + 5^{\circ} = 305^{\circ}

The hour hand continuously moves. It does not stay exactly on the 10 while the minute hand moves.

Calculate the new position of the minute hand after the manual rotation.

The new minute hand position is

60^{\circ} + 210^{\circ} = 270^{\circ}

The problem states the minute hand is pushed forward by exactly

210^{\circ}

Calculate the angle between the locked hour hand and the new minute hand position.

The difference is

305^{\circ} - 270^{\circ} = 35^{\circ}

Subtracting the smaller angular position from the larger one gives the acute interior angle between the hands.

Anahtar Kavram

Clock hand angular positioning, rotational displacement, and proportional hour-hand drift.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru