At what time between 7 and 8 O'clock will the hands of a clock be at right angle? (a) 19 (5)/(11

step 1 To solve the next question, it has been given that the R hand is in between 2 and 3. Okay, then

At what time between 7 and 8 O'clock will the hands of a...

Key Concepts

Angular Positions of Clock Hands

This involves computing the positions of the clock's hands based on time. The minute hand's position is directly proportional to the number of minutes past the hour, while the hour hand's position includes both the hour and the fraction due to the minutes passed. This concept is used to set up expressions that equate the desired angle difference.

Equation Setup for Time Calculation

Once the positions of the clock hands are expressed in terms of time, an equation can be set up to find the moments when the hands are at a particular angle. The equation incorporates the initial angular displacement and the relative speeds of the hands, and solving it provides the exact time at which the specified angular condition (such as a right angle) is met.

Clock Angle Problems

This concept involves determining the angle between the hour hand and the minute hand on an analog clock at a given time. It is foundational for solving problems that ask for times when the hands are at specific angles, such as 90° (right angle) or 180° (straight line).

Relative Angular Velocity

This concept pertains to the rates at which the hour hand and the minute hand move. The minute hand moves at a constant rate of 6° per minute while the hour hand moves at 0.5° per minute. Understanding how these speeds differ is crucial for calculating the angles between the hands over time.

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