At what time between 4: 30 and 5 will the hands of a clock be in a straight line? (a) 50 mins. p

step 1 Hello, again, now we can please try and error. If we did this for all four, we realize that B, 5

At what time between 4: 30 and 5 will the hands of a clock...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Angular Velocity of Clock Hands

This concept refers to the rate at which the minute and hour hands move on the clock. The minute hand moves 360 degrees in 60 minutes, while the hour hand moves 360 degrees in 12 hours. Understanding their degrees per minute (6 degrees for the minute hand and 0.5 degrees for the hour hand) is essential for analyzing the positions of the hands at any given time.

Relative Motion and Angle Difference

This involves understanding that the difference in the speeds of the clock hands is what determines how their positions change relative to each other. By calculating the relative angular speed, one can set up an equation to determine when the hands form a specific angle, such as being in a straight line.

Linear Relationship Between Time and Angular Displacement

Since both clock hands move at constant speeds, their angular positions increase linearly over time. By expressing these positions as functions of time, it becomes possible to solve for the time at which a given angular separation occurs. This concept provides the mathematical framework needed for problems involving the alignment of the clock hands.

Transcript

Please give Ace some feedback